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Author: Nathan Jacobson
Publisher: Courier Corporation
Published: 2013-09-16
Total Pages: 348
ISBN-13: 0486136795
DOWNLOAD EBOOKDIVDefinitive treatment of important subject in modern mathematics. Covers split semi-simple Lie algebras, universal enveloping algebras, classification of irreducible modules, automorphisms, simple Lie algebras over an arbitrary field, etc. Index. /div
Author: Nathan Jacobson
Publisher: Springer Science & Business Media
Published: 2009-12-09
Total Pages: 290
ISBN-13: 3642024297
DOWNLOAD EBOOKHere, the eminent algebraist, Nathan Jacobsen, concentrates on those algebras that have an involution. Although they appear in many contexts, these algebras first arose in the study of the so-called "multiplication algebras of Riemann matrices". Of particular interest are the Jordan algebras determined by such algebras, and thus their structure is discussed in detail. Two important concepts also dealt with are the universal enveloping algebras and the reduced norm. However, the largest part of the book is the fifth chapter, which focuses on involutorial simple algebras of finite dimension over a field.
Author: Nathan Jacobson
Publisher: Courier Corporation
Published: 2012-12-11
Total Pages: 530
ISBN-13: 0486135225
DOWNLOAD EBOOKA classic text and standard reference for a generation, this volume covers all undergraduate algebra topics, including groups, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. 1985 edition.
Author: N. Jacobson
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 557
ISBN-13: 1461236940
DOWNLOAD EBOOKThis 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.
Author: N. Jacobson
Publisher: Springer
Published: 2006-11-15
Total Pages: 120
ISBN-13: 3540374272
DOWNLOAD EBOOKAuthor: N. Jacobson
Publisher: Springer
Published: 1975
Total Pages: 304
ISBN-13:
DOWNLOAD EBOOKThe 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.
Author: Nathan Jacobson
Publisher: American Mathematical Soc.
Published: 1968-12-31
Total Pages: 464
ISBN-13: 082184640X
DOWNLOAD EBOOKThe 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, and Wigner to formulate the foundations of quantum mechanics. They are still useful and important in modern mathematical physics, as well as in Lie theory, geometry, and certain areas of analysis.
Author: Nathan Jacobson
Publisher: American Mathematical Soc.
Published: 1964
Total Pages: 311
ISBN-13: 0821810375
DOWNLOAD EBOOKThe main purpose of this volume is to give an account of the important developments in the theory of (non-commutative) rings. These are: the structure theory of rings without finiteness assumptions, cohomology of algebras, and structure and representation theory of non-semi-simple rings (Frobenius algebras, quasi-Frobenius rings).
Author: Nathan Jacobson
Publisher: American Mathematical Soc.
Published: 1943-12-31
Total Pages: 160
ISBN-13: 0821815024
DOWNLOAD EBOOKThe book is mainly concerned with the theory of rings in which both maximal and minimal conditions hold for ideals (except in the last chapter, where rings of the type of a maximal order in an algebra are considered). The central idea consists of representing rings as rings of endomorphisms of an additive group, which can be achieved by means of the regular representation.
Author: Nathan Jacobson
Publisher: Courier Corporation
Published: 2009-06-22
Total Pages: 530
ISBN-13: 0486471896
DOWNLOAD EBOOK"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"--Cover p. 4
