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Author: Carl Clifton Faith
Publisher: American Mathematical Soc.
ISBN: 0821836722
Category : Mathematics
Languages : en
Pages : 513
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Book Description
This book surveys more than 125 years of aspects of associative algebras, especially ring and module theory. It is the first to probe so extensively such a wealth of historical development. Moreover, the author brings the reader up to date, in particular through his report on the subject in the second half of the twentieth century. Included in the book are certain categorical properties from theorems of Frobenius and Stickelberger on the primary decomposition of finite Abelian formulations of the latter by Krull, Goldman, and others; Maschke's theorem on the representation theory of finite groups over a field; and the fundamental theorems of Wedderburn on the structure of finite dimensional algebras Goldie, and others. A special feature of the book is the in-depth study of rings with chain condition on annihilator ideals pioneered by Noether, Artin, and Jacobson and refined and extended by many later mathematicians. Two of the author's prior works, Algebra: Rings, Modules and Categories, I and II (Springer-Verlag, 1973), are devoted to the development of modern associative algebra and ring and module theory. Those bibliography of over 1,600 references and is exhaustively indexed. In addition to the mathematical survey, the author gives candid and descriptive impressions of the last half of the twentieth century in ''Part II: Snapshots of fellow graduate students at the University of Kentucky and at Purdue, Faith discusses his Fulbright-Nato Postdoctoral at Heidelberg and at the Institute for Advanced Study (IAS) at Princeton, his year as a visiting scholar at Berkeley, and the many acquaintances he met there and in subsequent travels in India, Europe, and most recently, Barcelona. Comments on the first edition: ''Researchers in algebra should find it both full references as to the origin and development of the theorem ... I know of no other work in print which does this as thoroughly and as broadly.'' --John O'Neill, University of Detroit at Mercy '' 'Part II: Snapshots of Mathematicians of my age and younger will relish reading 'Snapshots'.'' --James A. Huckaba, University of Missouri-Columbia
Author: Carl Clifton Faith
Publisher: American Mathematical Soc.
ISBN: 0821836722
Category : Mathematics
Languages : en
Pages : 513
Get Book Here
Book Description
This book surveys more than 125 years of aspects of associative algebras, especially ring and module theory. It is the first to probe so extensively such a wealth of historical development. Moreover, the author brings the reader up to date, in particular through his report on the subject in the second half of the twentieth century. Included in the book are certain categorical properties from theorems of Frobenius and Stickelberger on the primary decomposition of finite Abelian formulations of the latter by Krull, Goldman, and others; Maschke's theorem on the representation theory of finite groups over a field; and the fundamental theorems of Wedderburn on the structure of finite dimensional algebras Goldie, and others. A special feature of the book is the in-depth study of rings with chain condition on annihilator ideals pioneered by Noether, Artin, and Jacobson and refined and extended by many later mathematicians. Two of the author's prior works, Algebra: Rings, Modules and Categories, I and II (Springer-Verlag, 1973), are devoted to the development of modern associative algebra and ring and module theory. Those bibliography of over 1,600 references and is exhaustively indexed. In addition to the mathematical survey, the author gives candid and descriptive impressions of the last half of the twentieth century in ''Part II: Snapshots of fellow graduate students at the University of Kentucky and at Purdue, Faith discusses his Fulbright-Nato Postdoctoral at Heidelberg and at the Institute for Advanced Study (IAS) at Princeton, his year as a visiting scholar at Berkeley, and the many acquaintances he met there and in subsequent travels in India, Europe, and most recently, Barcelona. Comments on the first edition: ''Researchers in algebra should find it both full references as to the origin and development of the theorem ... I know of no other work in print which does this as thoroughly and as broadly.'' --John O'Neill, University of Detroit at Mercy '' 'Part II: Snapshots of Mathematicians of my age and younger will relish reading 'Snapshots'.'' --James A. Huckaba, University of Missouri-Columbia
Author: Viet Dung Nguyen
Publisher: American Mathematical Soc.
ISBN: 0821843702
Category : Mathematics
Languages : en
Pages : 377
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Book Description
The papers in this volume contain results in active research areas in the theory of rings and modules, including non commutative and commutative ring theory, module theory, representation theory, and coding theory.
Author: Sergio R. López-Permouth
Publisher: American Mathematical Soc.
ISBN: 1470435551
Category : Mathematics
Languages : en
Pages : 298
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Book Description
This volume, dedicated to Bruno J. Müller, a renowned algebraist, is a collection of papers that provide a snapshot of the diversity of themes and applications that interest algebraists today. The papers highlight the latest progress in ring and module research and present work done on the frontiers of the topics discussed. In addition, selected expository articles are included to give algebraists and other mathematicians, including graduate students, an accessible introduction to areas that may be outside their own expertise.
Author:
Publisher: Elsevier
ISBN: 0080532977
Category : Mathematics
Languages : en
Pages : 1185
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Book Description
Handbook of Algebra
Author: W. K. Nicholson
Publisher: Cambridge University Press
ISBN: 9780521815932
Category : Mathematics
Languages : en
Pages : 332
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Book Description
Provides an elementary account of the basic facts about quasi-Frobenius rings.
Author: David A. Cox
Publisher: American Mathematical Soc.
ISBN: 082182127X
Category : Mathematics
Languages : en
Pages : 498
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Book Description
Mirror symmetry began when theoretical physicists made some astonishing predictions about rational curves on quintic hypersurfaces in four-dimensional projective space. Understanding the mathematics behind these predictions has been a substantial challenge. This book is the first completely comprehensive monograph on mirror symmetry, covering the original observations by the physicists through the most recent progress made to date. Subjects discussed include toric varieties, Hodge theory, Kahler geometry, moduli of stable maps, Calabi-Yau manifolds, quantum cohomology, Gromov-Witten invariants, and the mirror theorem. This title features: numerous examples worked out in detail; an appendix on mathematical physics; an exposition of the algebraic theory of Gromov-Witten invariants and quantum cohomology; and, a proof of the mirror theorem for the quintic threefold.
Author: Jens Carsten Jantzen
Publisher: American Mathematical Soc.
ISBN: 9780821835272
Category : Mathematics
Languages : en
Pages : 652
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Book Description
Now back in print by the AMS, this is a significantly revised edition of a book originally published in 1987 by Academic Press. This book gives the reader an introduction to the theory of algebraic representations of reductive algebraic groups. To develop appropriate techniques, the first part of the book is an introduction to the general theory of representations of algebraic group schemes. Here, the author describes important basic notions: induction functors, cohomology,quotients, Frobenius kernels, and reduction mod $p$, among others. The second part of the book is devoted to the representation theory of reductive algebraic groups. It includes topics such as the description of simple modules, vanishing theorems, the Borel-Bott-Weil theorem and Weyl's character formula, andSchubert schemes and line bundles on them. For this revised edition the author added nearly 150 pages of new material describing some later developments, among them Schur algebras, Lusztig's conjecture and Kazhdan-Lusztig polynomials, tilting modules, and representations of quantum groups. He also made major revisions to parts of the old text. Jantzen's book continues to be the ultimate source of information on representations of algebraic groups in finite characteristics. It is suitable forgraduate students and research mathematicians interested in algebraic groups and their representations.
Author: S. K. Jain
Publisher: Oxford University Press
ISBN: 0191641545
Category : Mathematics
Languages : en
Pages :
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Book Description
This unique and comprehensive volume provides an up-to-date account of the literature on the subject of determining the structure of rings over which cyclic modules or proper cyclic modules have a finiteness condition or a homological property. The finiteness conditions and homological properties are closely interrelated in the sense that either hypothesis induces the other in some form. This is the first book to bring all of this important material on the subject together. Over the last 25 years or more numerous mathematicians have investigated rings whose factor rings or factor modules have a finiteness condition or a homological property. They made important contributions leading to new directions and questions, which are listed at the end of each chapter for the benefit of future researchers. There is a wealth of material on the topic which is combined in this book, it contains more than 200 references and is not claimed to be exhaustive. This book will appeal to graduate students, researchers, and professionals in algebra with a knowledge of basic noncommutative ring theory, as well as module theory and homological algebra, equivalent to a one-year graduate course in the theory of rings and modules.
Author: Stephen Wiggins
Publisher: American Mathematical Soc.
ISBN: 9780821871676
Category : Education
Languages : en
Pages : 538
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Book Description
This monograph, which grew out of a series of lectures delivered by Stephen Wiggins at the Fields Institute in early 1993, is concerned with the geometrical viewpoint of the global dynamics of nonlinear dynamical systems. With appropriate examples and concise explanations, Wiggins unites many different topics into one volume and makes a unique contribution to the field. Engineers, physicists, chemists, and mathematicians who work on issues related to the global dynamics of nonlinear dynamical systems will find these lectures very useful.
Author: Victor Guillemin
Publisher: American Mathematical Soc.
ISBN: 0821805029
Category : Mathematics
Languages : en
Pages : 362
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Book Description
During the last 20 years, ``localization'' has been one of the dominant themes in the area of equivariant differential geometry. Typical results are the Duistermaat-Heckman theory, the Berline-Vergne-Atiyah-Bott localization theorem in equivariant de Rham theory, and the ``quantization commutes with reduction'' theorem and its various corollaries. To formulate the idea that these theorems are all consequences of a single result involving equivariant cobordisms, the authors have developed a cobordism theory that allows the objects to be non-compact manifolds. A key ingredient in this non-compact cobordism is an equivariant-geometrical object which they call an ``abstract moment map''. This is a natural and important generalization of the notion of a moment map occurring in the theory of Hamiltonian dynamics. The book contains a number of appendices that include introductions to proper group-actions on manifolds, equivariant cohomology, Spin${^\mathrm{c}}$-structures, and stable complex structures. It is geared toward graduate students and research mathematicians interested in differential geometry. It is also suitable for topologists, Lie theorists, combinatorists, and theoretical physicists. Prerequisite is some expertise in calculus on manifolds and basic graduate-level differential geometry.
