Jacobson, Nathan 19101999
Overview
Works:  137 works in 903 publications in 6 languages and 10,033 library holdings 

Genres:  History Biography 
Roles:  Author, Editor, Contributor, Dedicatee, Other, Performer 
Classifications:  QA154.2, 512.89 
Publication Timeline
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Most widely held works about
Nathan Jacobson
 Hoffman, Stephen, Papers by Stephen P Hoffman( )
 Papers by Alfred L Putnam( )
 A personal history by Nathan Jacobson( Book )
 Nathan Jacobson (19101999) by Georgia Benkart( )
 Jacobson, Nathan : mathematics( )
 Medical College history file by Upstate Medical Center (N.Y.)( )
 In memoriam : Nathan Jacobson, 18571913( Book )
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Most widely held works by
Nathan Jacobson
Basic algebra by
Nathan Jacobson(
Book
)
39 editions published between 1974 and 2009 in English and held by 1,536 WorldCat member libraries worldwide
A classic text and standard reference for a generation, these two volumes are the work of Nathan Jacobson, an expert algebraist who taught at Yale for over three decades. The books are conceptually and theoretically oriented. Volume one explores all the topics addressed in undergraduate courses, while volume two comprises all of the subjects usually covered in a firstyear graduate course, revisiting and expanding on many topics from volume one. Each volume has exercises and insightful, carefully explained proofs
39 editions published between 1974 and 2009 in English and held by 1,536 WorldCat member libraries worldwide
A classic text and standard reference for a generation, these two volumes are the work of Nathan Jacobson, an expert algebraist who taught at Yale for over three decades. The books are conceptually and theoretically oriented. Volume one explores all the topics addressed in undergraduate courses, while volume two comprises all of the subjects usually covered in a firstyear graduate course, revisiting and expanding on many topics from volume one. Each volume has exercises and insightful, carefully explained proofs
Lectures in abstract algebra by
Nathan Jacobson(
Book
)
33 editions published between 1951 and 1976 in English and Undetermined and held by 1,260 WorldCat member libraries worldwide
The three volume Lectures are based on Jacobson's graduate lectures on algebra at John Hopkins and Yale in the 1940's and early 1950's, and are very careful, comprehensive and classical in style, giving a general treatment of abstract algebra. The first volume gives a comprehensive introduction to abstract algebra and its basic concepts. The second volume deals with the theory of vector spaces, accompanied by examples and exercises. The third and final volume addresses field theory and Galois theory, and is not an easy read for the casual student, but a serious student who works at the material will be repaid for their efforts. All volumes include a considerable number of exercises are given that vary greatly in difficulty, while the texts in general are exampledriven and userfriendly
33 editions published between 1951 and 1976 in English and Undetermined and held by 1,260 WorldCat member libraries worldwide
The three volume Lectures are based on Jacobson's graduate lectures on algebra at John Hopkins and Yale in the 1940's and early 1950's, and are very careful, comprehensive and classical in style, giving a general treatment of abstract algebra. The first volume gives a comprehensive introduction to abstract algebra and its basic concepts. The second volume deals with the theory of vector spaces, accompanied by examples and exercises. The third and final volume addresses field theory and Galois theory, and is not an easy read for the casual student, but a serious student who works at the material will be repaid for their efforts. All volumes include a considerable number of exercises are given that vary greatly in difficulty, while the texts in general are exampledriven and userfriendly
Lie algebras by
Nathan Jacobson(
Book
)
62 editions published between 1961 and 2013 in 5 languages and held by 1,089 WorldCat member libraries worldwide
Lie group theory, developed by M. Sophus Lie in the 19th century, ranks among the more important developments in modern mathematics. Lie algebras comprise a significant part of Lie group theory and are being actively studied today. This book, by Professor Nathan Jacobson of Yale, is the definitive treatment of the subject and can be used as a textbook for graduate courses. Chapter I introduces basic concepts that are necessary for an understanding of structure theory, while the following three chapters present the theory itself: solvable and nilpotent Lie algebras, Carlan's criterion and its consequences, and split semisimple Lie algebras. Chapter 5, on universal enveloping algebras, provides the abstract concepts underlying representation theory. Then the basic results on representation theory are given in three succeeding chapters: the theorem of AdoIwasawa, classification of irreducible modules, and characters of the irreducible modules. In Chapter 9 the automorphisms of semisimple Lie algebras over an algebraically closed field of characteristic zero are determined. These results are applied in Chapter 10 to the problems of sorting out the simple Lie algebras over an arbitrary field. The reader, to fully benefit from this tenth chapter, should have some knowledge about the notions of Galois theory and some of the results of the Wedderburn structure theory of associative algebras. Nathan Jacobson, presently Henry Ford II Professor of Mathematics at Yale University, is a wellknown authority in the field of abstract algebra. His book, Lie Algebras, is a classic handbook both for researchers and students. Though it presupposes a knowledge of linear algebra, it is not overly theoretical and can be readily used for selfstudy
62 editions published between 1961 and 2013 in 5 languages and held by 1,089 WorldCat member libraries worldwide
Lie group theory, developed by M. Sophus Lie in the 19th century, ranks among the more important developments in modern mathematics. Lie algebras comprise a significant part of Lie group theory and are being actively studied today. This book, by Professor Nathan Jacobson of Yale, is the definitive treatment of the subject and can be used as a textbook for graduate courses. Chapter I introduces basic concepts that are necessary for an understanding of structure theory, while the following three chapters present the theory itself: solvable and nilpotent Lie algebras, Carlan's criterion and its consequences, and split semisimple Lie algebras. Chapter 5, on universal enveloping algebras, provides the abstract concepts underlying representation theory. Then the basic results on representation theory are given in three succeeding chapters: the theorem of AdoIwasawa, classification of irreducible modules, and characters of the irreducible modules. In Chapter 9 the automorphisms of semisimple Lie algebras over an algebraically closed field of characteristic zero are determined. These results are applied in Chapter 10 to the problems of sorting out the simple Lie algebras over an arbitrary field. The reader, to fully benefit from this tenth chapter, should have some knowledge about the notions of Galois theory and some of the results of the Wedderburn structure theory of associative algebras. Nathan Jacobson, presently Henry Ford II Professor of Mathematics at Yale University, is a wellknown authority in the field of abstract algebra. His book, Lie Algebras, is a classic handbook both for researchers and students. Though it presupposes a knowledge of linear algebra, it is not overly theoretical and can be readily used for selfstudy
Structure of rings by
Nathan Jacobson(
Book
)
57 editions published between 1956 and 1997 in 3 languages and held by 891 WorldCat member libraries worldwide
The main purpose of this volume is to give an account of the important developments in the theory of (noncommutative) rings. These are: the structure theory of rings without finiteness assumptions, cohomology of algebras, and structure and representation theory of nonsemisimple rings (Frobenius algebras, quasiFrobenius rings)
57 editions published between 1956 and 1997 in 3 languages and held by 891 WorldCat member libraries worldwide
The main purpose of this volume is to give an account of the important developments in the theory of (noncommutative) rings. These are: the structure theory of rings without finiteness assumptions, cohomology of algebras, and structure and representation theory of nonsemisimple rings (Frobenius algebras, quasiFrobenius rings)
The theory of rings by
Nathan Jacobson(
Book
)
60 editions published between 1943 and 2014 in 3 languages and held by 658 WorldCat member libraries worldwide
Groups and endomoprphism; Vector spaces; Noncommutative principal ideal domains; Strucutre of rings of endomorphisms and of abstract rings; Algebras over a field; Multiplicative ideal theory
60 editions published between 1943 and 2014 in 3 languages and held by 658 WorldCat member libraries worldwide
Groups and endomoprphism; Vector spaces; Noncommutative principal ideal domains; Strucutre of rings of endomorphisms and of abstract rings; Algebras over a field; Multiplicative ideal theory
PIalgebras : an introduction by
Nathan Jacobson(
Book
)
20 editions published between 1975 and 2008 in 3 languages and held by 605 WorldCat member libraries worldwide
20 editions published between 1975 and 2008 in 3 languages and held by 605 WorldCat member libraries worldwide
Structure and representations of Jordan algebras by
Nathan Jacobson(
Book
)
19 editions published between 1968 and 2012 in English and Undetermined and held by 538 WorldCat member libraries worldwide
The purpose of this book is to give a comprehensive account of the structure and representation theory of Jordan algebras over a field of characteristic not two
19 editions published between 1968 and 2012 in English and Undetermined and held by 538 WorldCat member libraries worldwide
The purpose of this book is to give a comprehensive account of the structure and representation theory of Jordan algebras over a field of characteristic not two
Exceptional Lie algebras by
Nathan Jacobson(
Book
)
13 editions published between 1971 and 2010 in English and held by 421 WorldCat member libraries worldwide
13 editions published between 1971 and 2010 in English and held by 421 WorldCat member libraries worldwide
Finitedimensional division algebras over fields by
Nathan Jacobson(
Book
)
21 editions published between 1996 and 2014 in 3 languages and held by 392 WorldCat member libraries worldwide
Finitedimensional division algebras over fields determine, by the Wedderburn Theorem, the semisimple finitedimensional algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the BrauerSeveri varieties. The book concentrates on those algebras that have an involution. Algebras with involution appear in many contexts; they arose first in the study of the socalled "multiplication algebras of Riemann matrices". The largest part of the book is the fifth chapter, dealing with involutorial simple algebras of finite dimension over a field. Of particular interest are the Jordan algebras determined by these algebras with involution; their structure is discussed. Two important concepts of these algebras with involution are the universal enveloping algebras and the reduced norm
21 editions published between 1996 and 2014 in 3 languages and held by 392 WorldCat member libraries worldwide
Finitedimensional division algebras over fields determine, by the Wedderburn Theorem, the semisimple finitedimensional algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the BrauerSeveri varieties. The book concentrates on those algebras that have an involution. Algebras with involution appear in many contexts; they arose first in the study of the socalled "multiplication algebras of Riemann matrices". The largest part of the book is the fifth chapter, dealing with involutorial simple algebras of finite dimension over a field. Of particular interest are the Jordan algebras determined by these algebras with involution; their structure is discussed. Two important concepts of these algebras with involution are the universal enveloping algebras and the reduced norm
Gesammelte Abhandlungen = Collected papers by
Emmy Noether(
Book
)
20 editions published between 1982 and 2013 in 4 languages and held by 296 WorldCat member libraries worldwide
Résumé
20 editions published between 1982 and 2013 in 4 languages and held by 296 WorldCat member libraries worldwide
Résumé
Basic algebra I by
Nathan Jacobson(
Book
)
37 editions published between 1973 and 2009 in English and Undetermined and held by 287 WorldCat member libraries worldwide
"Explores all of the topics typically covered in undergraduate courses including the rudiments of set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra"Page 4 of cover
37 editions published between 1973 and 2009 in English and Undetermined and held by 287 WorldCat member libraries worldwide
"Explores all of the topics typically covered in undergraduate courses including the rudiments of set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra"Page 4 of cover
Lectures in abstract algebra by
Nathan Jacobson(
Book
)
53 editions published between 1951 and 2013 in English and Undetermined and held by 261 WorldCat member libraries worldwide
The present volume is the second in the author's series of three dealing with abstract algebra. For an understanding of this volume a certain familiarity with the basic concepts treated in Volume I: groups, rings, fields, homomorphisms, is presup posed. However, we have tried to make this account of linear algebra independent of a detailed knowledge of our first volume. References to specific results are given occasionally but some of the fundamental concepts needed have been treated again. In short, it is hoped that this volume can be read with complete understanding by any student who is mathematically sufficiently mature and who has a familiarity with the standard notions of modern algebra. Our point of view in the present volume is basically the abstract conceptual one. However, from time to time we have deviated somewhat from this. Occasionally formal calculational methods yield sharper results. Moreover, the results of linear algebra are not an end in themselves but are essential tools for use in other branches of mathematics and its applications. It is therefore useful to have at hand methods which are constructive and which can be applied in numerical problems. These methods sometimes necessitate a somewhat lengthier discussion but we have felt that their presentation is justified on the grounds indicated. A stu dent well versed in abstract algebra will undoubtedly observe short cuts. Some of these have been indicated in footnotes. We have included a large number of exercises in the text
53 editions published between 1951 and 2013 in English and Undetermined and held by 261 WorldCat member libraries worldwide
The present volume is the second in the author's series of three dealing with abstract algebra. For an understanding of this volume a certain familiarity with the basic concepts treated in Volume I: groups, rings, fields, homomorphisms, is presup posed. However, we have tried to make this account of linear algebra independent of a detailed knowledge of our first volume. References to specific results are given occasionally but some of the fundamental concepts needed have been treated again. In short, it is hoped that this volume can be read with complete understanding by any student who is mathematically sufficiently mature and who has a familiarity with the standard notions of modern algebra. Our point of view in the present volume is basically the abstract conceptual one. However, from time to time we have deviated somewhat from this. Occasionally formal calculational methods yield sharper results. Moreover, the results of linear algebra are not an end in themselves but are essential tools for use in other branches of mathematics and its applications. It is therefore useful to have at hand methods which are constructive and which can be applied in numerical problems. These methods sometimes necessitate a somewhat lengthier discussion but we have felt that their presentation is justified on the grounds indicated. A stu dent well versed in abstract algebra will undoubtedly observe short cuts. Some of these have been indicated in footnotes. We have included a large number of exercises in the text
Lectures in abstract algebra by
Nathan Jacobson(
Book
)
70 editions published between 1951 and 1977 in 3 languages and held by 246 WorldCat member libraries worldwide
The present volume is the first of three that will be published under the general title Lectures in Abstract Algebra. These vol umes are based on lectures which the author has given during the past ten years at the University of North Carolina, at The Johns Hopkins University, and at Yale "University. The general plan of the work IS as follows: The present first volume gives an introduction to abstract algebra and gives an account of most of the important algebraIc concepts. In a treatment of this type it is impossible to give a comprehensive account of the topics which are introduced. Nevertheless we have tried to go beyond the foundations and elementary properties of the algebraic sys tems. This has necessitated a certain amount of selection and omission. We feel that even at the present stage a deeper under standing of a few topics is to be preferred to a superficial under standing of many. The second and third volumes of this work will be more special ized in nature and will attempt to give comprehensive accounts of the topics which they treat. Volume II will bear the title Linear Algebra and will deal with the theorv of vectQ!_JlP.a. ces. ... Volume III, The Theory of Fields and Galois Theory, will be con cerned with the algebraic structure offieras and with valuations of fields. All three volumes have been planned as texts for courses
70 editions published between 1951 and 1977 in 3 languages and held by 246 WorldCat member libraries worldwide
The present volume is the first of three that will be published under the general title Lectures in Abstract Algebra. These vol umes are based on lectures which the author has given during the past ten years at the University of North Carolina, at The Johns Hopkins University, and at Yale "University. The general plan of the work IS as follows: The present first volume gives an introduction to abstract algebra and gives an account of most of the important algebraIc concepts. In a treatment of this type it is impossible to give a comprehensive account of the topics which are introduced. Nevertheless we have tried to go beyond the foundations and elementary properties of the algebraic sys tems. This has necessitated a certain amount of selection and omission. We feel that even at the present stage a deeper under standing of a few topics is to be preferred to a superficial under standing of many. The second and third volumes of this work will be more special ized in nature and will attempt to give comprehensive accounts of the topics which they treat. Volume II will bear the title Linear Algebra and will deal with the theorv of vectQ!_JlP.a. ces. ... Volume III, The Theory of Fields and Galois Theory, will be con cerned with the algebraic structure offieras and with valuations of fields. All three volumes have been planned as texts for courses
Lectures in abstract algebra by
Nathan Jacobson(
Book
)
54 editions published between 1951 and 2000 in 3 languages and held by 238 WorldCat member libraries worldwide
The present volume completes the series of texts on algebra which the author began more than ten years ago. The account of field theory and Galois theory which we give here is based on the notions and results of general algebra which appear in our first volume and on the more elementary parts of the second volume, dealing with linear algebra. The level of the present work is roughly the same as that of Volume II. In preparing this book we have had a number of objectives in mind. First and foremost has been that of presenting the basic field theory which is essential for an understanding of modern algebraic number theory, ring theory, and algebraic geometry. The parts of the book concerned with this aspect of the subject are Chapters I, IV, and V dealing respectively with finite dimen sional field extensions and Galois theory, general structure theory of fields, and valuation theory. Also the results of Chapter IlIon abelian extensions, although of a somewhat specialized nature, are of interest in number theory. A second objective of our ac count has been to indicate the links between the present theory of fields and the classical problems which led to its development
54 editions published between 1951 and 2000 in 3 languages and held by 238 WorldCat member libraries worldwide
The present volume completes the series of texts on algebra which the author began more than ten years ago. The account of field theory and Galois theory which we give here is based on the notions and results of general algebra which appear in our first volume and on the more elementary parts of the second volume, dealing with linear algebra. The level of the present work is roughly the same as that of Volume II. In preparing this book we have had a number of objectives in mind. First and foremost has been that of presenting the basic field theory which is essential for an understanding of modern algebraic number theory, ring theory, and algebraic geometry. The parts of the book concerned with this aspect of the subject are Chapters I, IV, and V dealing respectively with finite dimen sional field extensions and Galois theory, general structure theory of fields, and valuation theory. Also the results of Chapter IlIon abelian extensions, although of a somewhat specialized nature, are of interest in number theory. A second objective of our ac count has been to indicate the links between the present theory of fields and the classical problems which led to its development
Basic Algebra by
Nathan Jacobson(
Book
)
40 editions published between 1980 and 2009 in 3 languages and held by 208 WorldCat member libraries worldwide
This classic text and standard reference comprises all subjects of a firstyear graduatelevel course, including indepth coverage of groups and polynomials and extensive use of categories and functors
40 editions published between 1980 and 2009 in 3 languages and held by 208 WorldCat member libraries worldwide
This classic text and standard reference comprises all subjects of a firstyear graduatelevel course, including indepth coverage of groups and polynomials and extensive use of categories and functors
Collected mathematical papers by
Nathan Jacobson(
Book
)
5 editions published in 1989 in English and held by 177 WorldCat member libraries worldwide
5 editions published in 1989 in English and held by 177 WorldCat member libraries worldwide
Lectures on quadratic Jordan algebras by
Nathan Jacobson(
Book
)
7 editions published between 1969 and 1979 in English and Undetermined and held by 148 WorldCat member libraries worldwide
7 editions published between 1969 and 1979 in English and Undetermined and held by 148 WorldCat member libraries worldwide
Collected mathematical papers by
Nathan Jacobson(
Book
)
3 editions published in 1989 in Undetermined and English and held by 64 WorldCat member libraries worldwide
3 editions published in 1989 in Undetermined and English and held by 64 WorldCat member libraries worldwide
Lectures in abstract algebra by
Nathan Jacobson(
Book
)
24 editions published between 1951 and 1975 in English and Undetermined and held by 59 WorldCat member libraries worldwide
24 editions published between 1951 and 1975 in English and Undetermined and held by 59 WorldCat member libraries worldwide
Nathan Jacobson, Collected mathematical papers by
Nathan Jacobson(
)
2 editions published in 1989 in English and held by 56 WorldCat member libraries worldwide
This collection contains all my published papers, both research and expository, that were published from 1934 to 1988. The research papers arranged in chronological order appear in Volume I and II and in the first part of Volume III. The expository papers, which are mainly reports presented at conferences, appear in chronological order in the last part of Volume III. Volume I covers the period 1910 to 1947, the year I moved to Yale, Volume II covers the period 1947 to 1965 when I became Chairman of the Department at Yale and Volume III covers the period from 1965 to 1989, which goes beyond my assumption of an emeritus status in 1981. I have divided the time interval covered in each volume into subintervals preceded by an account of my personal history during this period, and a commentary on the research papers published in the period. I have omitted commentaries on the expository papers and have sorted out the commentaries on the research papers according to the principal fields of my research. The personal history has been based on my recollections, checked against written documentation in my file of letters as well as diaries. One of these was a diary I kept of my trip to the USSR in 1961; the others were diaries Florie (Florence) kept during other major visits abroad. I have also consulted Professor A.W. Tucker on historical details on Princeton during the 1930's
2 editions published in 1989 in English and held by 56 WorldCat member libraries worldwide
This collection contains all my published papers, both research and expository, that were published from 1934 to 1988. The research papers arranged in chronological order appear in Volume I and II and in the first part of Volume III. The expository papers, which are mainly reports presented at conferences, appear in chronological order in the last part of Volume III. Volume I covers the period 1910 to 1947, the year I moved to Yale, Volume II covers the period 1947 to 1965 when I became Chairman of the Department at Yale and Volume III covers the period from 1965 to 1989, which goes beyond my assumption of an emeritus status in 1981. I have divided the time interval covered in each volume into subintervals preceded by an account of my personal history during this period, and a commentary on the research papers published in the period. I have omitted commentaries on the expository papers and have sorted out the commentaries on the research papers according to the principal fields of my research. The personal history has been based on my recollections, checked against written documentation in my file of letters as well as diaries. One of these was a diary I kept of my trip to the USSR in 1961; the others were diaries Florie (Florence) kept during other major visits abroad. I have also consulted Professor A.W. Tucker on historical details on Princeton during the 1930's
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Related Identities
 American Mathematical Society Editor
 Noether, Emmy 18821935 Author
 SpringerLink (Service en ligne)
 Aleksandrov, Pavel Sergeevitch 18961982 Author of introduction
 Saltman, David J. Other Editor
 Zariski, Oscar 18991986
 Du Val, Patrick 1903
 Institute for Advanced Study (Princeton, N.J.). School of Mathematics
 Amitsur, Shimshon A. Other Editor
 Albert, Abraham Adrian (19051972) Author
Useful Links
Associated Subjects
Algebra Algebra, Abstract Algebraic fields Algebraic functions American Civil War (18611865) American Mathematical Society Canada College teachers Cook, George W Division algebras Galois theory Geneva Medical College Geometry Geometry, NonEuclidean Group theory Hille, Einar, Jacobson, Nathan, Jordan algebras Kakutani, Shizuo, Lie algebras Mathematicians Mathematics MathematicsStudy and teaching Medical colleges Medicine MedicineStudy and teaching Military operations, Naval New York (State) New York (State)Syracuse Physicians Public health Rings (Algebra) Schools Scientists Social conditions Students Syracuse University.College of Medicine United States Universities and collegesAlumni and alumnae Universities and collegesFaculty Upstate Medical Center (N.Y.) WomenHealth and hygiene Yale University
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Alternative Names
Džekobson, N.
Džekobson, N. 19101999
Jacobson, N.
Jacobson, N. 1910
Jacobson, N. 19101999
Jacobson, N. (Nathan), 1910
Jacobson, N. (Nathan), 19101999
Jacobson, Nathan
Jacobson, Nathan 1910
Nathan Jacobson matemático estadounidense
Nathan Jacobson matematico statunitense
Nathan Jacobson mathématicien américain
Nathan Jacobson USamerikanischer Mathematiker
Nathan Jacobson wiskundige uit Keizerrijk Rusland (19101999)
Джекобсон, Н..
Натан Джекобсон американский математик
Նաթան Ջեյքոբսոն
נתן ג'ייקובסון
נתן ג'ייקובסון מתמטיקאי אמריקאי
ناتان جیکوبسون ریاضیدان آمریکایی
네이선 제이컵슨
ジャコブソン
内森·雅各布森
纳森·雅各布森
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