Jacobson, Nathan 19101999
Overview
Works:  134 works in 877 publications in 6 languages and 10,001 library holdings 

Genres:  History Biography 
Roles:  Author, Editor, Other, Contributor, Dedicatee, Performer 
Classifications:  QA154.2, 512.89 
Publication Timeline
.
Most widely held works about
Nathan Jacobson
 Papers by Alfred L Putnam( )
 Jacobson, Nathan : mathematics( )
 A personal history by Nathan Jacobson( Book )
 Nathan Jacobson (19101999) by Georgia Benkart( )
 Medical College history file by Upstate Medical Center (N.Y.)( )
 Hoffman, Stephen, Papers by Stephen P Hoffman( )
 In memoriam : Nathan Jacobson, 18571913( Book )
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Most widely held works by
Nathan Jacobson
Lectures in abstract algebra by
Nathan Jacobson(
Book
)
153 editions published between 1951 and 2013 in 3 languages and held by 1,534 WorldCat member libraries worldwide
V.1: Basic concepts; v.2: Linear algebra; v.3: Theory of fields and galois theory
153 editions published between 1951 and 2013 in 3 languages and held by 1,534 WorldCat member libraries worldwide
V.1: Basic concepts; v.2: Linear algebra; v.3: Theory of fields and galois theory
Basic algebra by
Nathan Jacobson(
Book
)
39 editions published between 1974 and 2009 in English and held by 1,380 WorldCat member libraries worldwide
Volume I of a pair of classic texts? and standard references for a generation? this book is the work of an expert algebraist who taught at Yale for two decades. Volume I covers all undergraduate topics, including groups, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. 1985 edition
39 editions published between 1974 and 2009 in English and held by 1,380 WorldCat member libraries worldwide
Volume I of a pair of classic texts? and standard references for a generation? this book is the work of an expert algebraist who taught at Yale for two decades. Volume I covers all undergraduate topics, including groups, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. 1985 edition
Lie algebras by
Nathan Jacobson(
Book
)
62 editions published between 1961 and 2013 in 5 languages and held by 1,002 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 1,002 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
)
64 editions published between 1956 and 1997 in 3 languages and held by 870 WorldCat member libraries worldwide
64 editions published between 1956 and 1997 in 3 languages and held by 870 WorldCat member libraries worldwide
The theory of rings by
Nathan Jacobson(
Book
)
58 editions published between 1943 and 2014 in 3 languages and held by 617 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
58 editions published between 1943 and 2014 in 3 languages and held by 617 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
Structure and representations of Jordan algebras by
Nathan Jacobson(
Book
)
18 editions published between 1968 and 2008 in English and Undetermined and held by 516 WorldCat member libraries worldwide
The theory of Jordan algebras has played important roles behind the scenes of several areas of mathematics. Jacobson's book has long been the definitive treatment of the subject. It covers foundational material, structure theory, and representation theory for Jordan algebras. Of course, there are immediate connections with Lie algebras, which Jacobson details in Chapter 8. Of particular continuing interest is the discussion of exceptional Jordan algebras, which serve to explain the exceptional Lie algebras and Lie groups. Jordan algebras originally arose in the attempts by Jordan, von Neumann
18 editions published between 1968 and 2008 in English and Undetermined and held by 516 WorldCat member libraries worldwide
The theory of Jordan algebras has played important roles behind the scenes of several areas of mathematics. Jacobson's book has long been the definitive treatment of the subject. It covers foundational material, structure theory, and representation theory for Jordan algebras. Of course, there are immediate connections with Lie algebras, which Jacobson details in Chapter 8. Of particular continuing interest is the discussion of exceptional Jordan algebras, which serve to explain the exceptional Lie algebras and Lie groups. Jordan algebras originally arose in the attempts by Jordan, von Neumann
Exceptional Lie algebras by
Nathan Jacobson(
Book
)
20 editions published between 1957 and 2017 in English and held by 429 WorldCat member libraries worldwide
"This volume presents a set of models for the exceptional Lie algebras over algebraically closed fieldsof characteristic O and over the field of real numbers. The models given are based on the algebras ofCayley numbers (octonions) and on exceptional Jordan algebras. They are also valid forcharacteristics p * 2. The book also provides an introduction to the problem of forms of exceptionalsimple Lie algebras, especially the exceptional D4 's, ? 6 's, and ? 7 's. These are studied by means ofconcrete realizations of the automorphism groups.Exceptional Lie Algebras is a useful tool for the mathematical public in generalespecially thoseinterested in the classification of Lie algebras or groupsand for theoretical physicists."Provided by publisher
20 editions published between 1957 and 2017 in English and held by 429 WorldCat member libraries worldwide
"This volume presents a set of models for the exceptional Lie algebras over algebraically closed fieldsof characteristic O and over the field of real numbers. The models given are based on the algebras ofCayley numbers (octonions) and on exceptional Jordan algebras. They are also valid forcharacteristics p * 2. The book also provides an introduction to the problem of forms of exceptionalsimple Lie algebras, especially the exceptional D4 's, ? 6 's, and ? 7 's. These are studied by means ofconcrete realizations of the automorphism groups.Exceptional Lie Algebras is a useful tool for the mathematical public in generalespecially thoseinterested in the classification of Lie algebras or groupsand for theoretical physicists."Provided by publisher
PIalgebras : an introduction by
Nathan Jacobson(
Book
)
20 editions published between 1975 and 2008 in 3 languages and held by 426 WorldCat member libraries worldwide
20 editions published between 1975 and 2008 in 3 languages and held by 426 WorldCat member libraries worldwide
Finitedimensional division algebras over fields by
Nathan Jacobson(
Book
)
19 editions published between 1996 and 2014 in 3 languages and held by 334 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
19 editions published between 1996 and 2014 in 3 languages and held by 334 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
)
19 editions published between 1982 and 2013 in 4 languages and held by 297 WorldCat member libraries worldwide
Résumé
19 editions published between 1982 and 2013 in 4 languages and held by 297 WorldCat member libraries worldwide
Résumé
Basic algebra I by
Nathan Jacobson(
Book
)
35 editions published between 1973 and 2009 in English and Undetermined and held by 255 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
35 editions published between 1973 and 2009 in English and Undetermined and held by 255 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
)
54 editions published between 1951 and 2013 in English and Undetermined and held by 202 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
54 editions published between 1951 and 2013 in English and Undetermined and held by 202 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
Basic Algebra by
Nathan Jacobson(
Book
)
36 editions published between 1980 and 2009 in 3 languages and held by 201 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
36 editions published between 1980 and 2009 in 3 languages and held by 201 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
Lectures in abstract algebra by
Nathan Jacobson(
Book
)
57 editions published between 1951 and 2000 in English and German and held by 183 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
57 editions published between 1951 and 2000 in English and German and held by 183 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
Collected mathematical papers by
Nathan Jacobson(
Book
)
7 editions published in 1989 in English and held by 179 WorldCat member libraries worldwide
7 editions published in 1989 in English and held by 179 WorldCat member libraries worldwide
Lectures on quadratic Jordan algebras by
Nathan Jacobson(
Book
)
10 editions published between 1969 and 1979 in English and Undetermined and held by 149 WorldCat member libraries worldwide
10 editions published between 1969 and 1979 in English and Undetermined and held by 149 WorldCat member libraries worldwide
Collected mathematical papers by
Nathan Jacobson(
Book
)
10 editions published in 1989 in 3 languages and held by 84 WorldCat member libraries worldwide
10 editions published in 1989 in 3 languages and held by 84 WorldCat member libraries worldwide
Theory of fields and Galois theory by
Nathan Jacobson(
Book
)
5 editions published between 1964 and 1980 in English and Undetermined and held by 49 WorldCat member libraries worldwide
Band 3
5 editions published between 1964 and 1980 in English and Undetermined and held by 49 WorldCat member libraries worldwide
Band 3
Collected mathematical papers by
Nathan Jacobson(
Book
)
7 editions published in 1989 in English and German and held by 47 WorldCat member libraries worldwide
7 editions published in 1989 in English and German and held by 47 WorldCat member libraries worldwide
A personal history by
Nathan Jacobson(
Book
)
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
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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
 Institute for Advanced Study (Princeton, N.J.). School of Mathematics
 Amitsur, Shimshon A. Other Editor
 Zariski, Oscar 18991986
 Du Val, Patrick 1903
 Albert, Abraham Adrian (19051972) Author
Useful Links
Associated Subjects
Algebra Algebra, Abstract Algebraic fields Algebraic functions Algebras, Linear 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
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
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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