WorldCat Identities

Jacobson, Nathan 1910-1999

Overview
Works: 137 works in 890 publications in 6 languages and 10,042 library holdings
Genres: History  Biography 
Roles: Author, Editor, Other, Dedicatee, Contributor, Performer
Classifications: QA154.2, 512.89
Publication Timeline
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Most widely held works about Nathan Jacobson
 
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Most widely held works by Nathan Jacobson
Basic algebra by Nathan Jacobson( Book )

38 editions published between 1974 and 2009 in English and held by 1,542 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
Lectures in abstract algebra by Nathan Jacobson( Book )

33 editions published between 1951 and 1976 in English and Undetermined and held by 1,270 WorldCat member libraries worldwide

V.1: Basic concepts; v.2: Linear algebra; v.3: Theory of fields and galois theory
Lie algebras by Nathan Jacobson( Book )

63 editions published between 1961 and 2013 in 5 languages and held by 1,100 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 semi-simple 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 Ado-Iwasawa, classification of irreducible modules, and characters of the irreducible modules. In Chapter 9 the automorphisms of semi-simple 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 well-known 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 self-study
Structure of rings by Nathan Jacobson( Book )

58 editions published between 1956 and 1997 in 3 languages and held by 888 WorldCat member libraries worldwide

The theory of rings by Nathan Jacobson( Book )

59 editions published between 1943 and 2014 in 3 languages and held by 663 WorldCat member libraries worldwide

Groups and endomoprphism; Vector spaces; Non-commutative principal ideal domains; Strucutre of rings of endomorphisms and of abstract rings; Algebras over a field; Multiplicative ideal theory
PI-algebras : an introduction by Nathan Jacobson( Book )

20 editions published between 1975 and 2008 in 3 languages and held by 582 WorldCat member libraries worldwide

Structure and representations of Jordan algebras by Nathan Jacobson( Book )

21 editions published between 1968 and 2012 in English and Undetermined and held by 546 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 )

13 editions published between 1971 and 2010 in English and held by 422 WorldCat member libraries worldwide

Finite-dimensional division algebras over fields by Nathan Jacobson( Book )

20 editions published between 1996 and 2014 in 3 languages and held by 389 WorldCat member libraries worldwide

Finite-dimensional division algebras over fields determine, by the Wedderburn Theorem, the semi-simple finite-dimensional algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the Brauer-Severi 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 so-called "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 300 WorldCat member libraries worldwide

Résumé
Basic algebra I by Nathan Jacobson( Book )

36 editions published between 1973 and 2009 in English and Undetermined and held by 288 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 264 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 )

76 editions published between 1951 and 1977 in 3 languages and held by 254 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 )

53 editions published between 1951 and 2000 in English and German and held by 232 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 )

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 first-year graduate-level course, including in-depth 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 178 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 149 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

Nathan Jacobson, Collected mathematical papers by Nathan Jacobson( )

2 editions published in 1989 in English and held by 53 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
Lectures in abstract algebra by Nathan Jacobson( Book )

33 editions published between 1951 and 1975 in English and Undetermined and held by 47 WorldCat member libraries worldwide

 
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Basic algebraBasic algebra I
Alternative Names
Džekobson, N.

Džekobson, N. 1910-1999

Jacobson, N.

Jacobson, N. 1910-

Jacobson, N. 1910-1999

Jacobson, N. (Nathan), 1910-

Jacobson, N. (Nathan), 1910-1999

Jacobson, Nathan

Jacobson, Nathan 1910-

Nathan Jacobson matemático estadounidense

Nathan Jacobson matematico statunitense

Nathan Jacobson mathématicien américain

Nathan Jacobson US-amerikanischer Mathematiker

Nathan Jacobson wiskundige uit Keizerrijk Rusland (1910-1999)

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

Languages
English (585)

German (17)

Russian (14)

Italian (3)

French (1)

Germanic (1)

Covers
Lie algebrasPI-algebras : an introductionStructure and representations of Jordan algebrasExceptional Lie algebrasFinite-dimensional division algebras over fieldsGesammelte Abhandlungen = Collected papersBasic algebra IBasic Algebra