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Author: Carl Clifton Faith Publisher: American Mathematical Soc. ISBN: 0821836722 Category : Mathematics Languages : en Pages : 513
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 Faith Publisher: American Mathematical Society(RI) ISBN: Category : Mathematics Languages : en Pages : 480
Book Description
Surveys over 125 years of associative algebras, focusing on ring and module theory. Topics of discussion in part one include categorical properties from theorems of Frobenius and Stickelberger on the primary decomposition of finite Abelian groups; Hilbert's basis theorem and his Nullstellensatz; the modern formulations of Hillbert's theorem by Krull and Goldman; Maschke's theorem on the representation theory of finite groups over a field; the fundamental theorems of Wedderburn on the structure of finite dimensional algebras and finite skew fields; and their extensions by Braver, Kaplansky, Chevally, and Goldie. Also included is a study of rings with chain condition on annihilator ideals pioneered by Noether, Artin, and Jacobson and refined and extended by many later mathematicians. Part two contains Faith's (professor emeritus, Rutgers U.) impressions of some mathematical friends and places from the last half of the 20th century. Annotation copyrighted by Book News, Inc., Portland, OR.
Author: Carl Clifton Faith Publisher: American Mathematical Soc. ISBN: 0821836722 Category : Mathematics Languages : en Pages : 513
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: Michiel Hazewinkel Publisher: Springer Science & Business Media ISBN: 9781402026904 Category : Mathematics Languages : en Pages : 396
Book Description
The text of the first volume of the book covers the major topics in ring and module theory and includes both fundamental classical results and more recent developments. The basic tools of investigation are methods from the theory of modules, which allow a very simple and clear approach both to classical and new results. An unusual main feature of this book is the use of the technique of quivers for studying the structure of rings. A considerable part of the first volume of the book is devoted to a study of special classes of rings and algebras, such as serial rings, hereditary rings, semidistributive rings and tiled orders. Many results of this text until now have been available in journal articles only. This book is aimed at graduate and post-graduate students and for all mathematicians who use algebraic techniques in their work. This is a self-contained book which is intended to be a modern textbook on the structure theory of associative rings and algebras and is suitable for independent study.
Author: Stuart A. Steinberg Publisher: Springer Science & Business Media ISBN: 1441917217 Category : Mathematics Languages : en Pages : 639
Book Description
This book provides an exposition of the algebraic aspects of the theory of lattice-ordered rings and lattice-ordered modules. All of the background material on rings, modules, and lattice-ordered groups necessary to make the work self-contained and accessible to a variety of readers is included. Filling a gap in the literature, Lattice-Ordered Rings and Modules may be used as a textbook or for self-study by graduate students and researchers studying lattice-ordered rings and lattice-ordered modules. Steinberg presents the material through 800+ extensive examples of varying levels of difficulty along with numerous exercises at the end of each section. Key topics include: lattice-ordered groups, rings, and fields; archimedean $l$-groups; f-rings and larger varieties of $l$-rings; the category of f-modules; various commutativity results.
Author: A. Giambruno Publisher: American Mathematical Soc. ISBN: 0821858254 Category : Mathematics Languages : en Pages : 283
Book Description
"This volume represents the proceedings of the conference on Groups, Rings and Group Rings, held July 28-August 2, 2008, in Ubatuba, Brazil. Papers in this volume contain results in active research areas in the theory of groups, group rings and algebras (including noncommutative rings), polynomial identities, Lie algebras and superalgebras. In particular, topics such as growth functions on varieties, groups of units in group rings, representation theory of Lie algebras, Jordan, alternative and Leibniz algebras, graded identities, automorphisms of trees, and partial actions, are discussed."--Publisher's website.
Author: Grigore Calugareanu Publisher: Springer Science & Business Media ISBN: 9780792349181 Category : Mathematics Languages : en Pages : 226
Book Description
Each undergraduate course of algebra begins with basic notions and results concerning groups, rings, modules and linear algebra. That is, it begins with simple notions and simple results. Our intention was to provide a collection of exercises which cover only the easy part of ring theory, what we have named the "Basics of Ring Theory". This seems to be the part each student or beginner in ring theory (or even algebra) should know - but surely trying to solve as many of these exercises as possible independently. As difficult (or impossible) as this may seem, we have made every effort to avoid modules, lattices and field extensions in this collection and to remain in the ring area as much as possible. A brief look at the bibliography obviously shows that we don't claim much originality (one could name this the folklore of ring theory) for the statements of the exercises we have chosen (but this was a difficult task: indeed, the 28 titles contain approximatively 15.000 problems and our collection contains only 346). The real value of our book is the part which contains all the solutions of these exercises. We have tried to draw up these solutions as detailed as possible, so that each beginner can progress without skilled help. The book is divided in two parts each consisting of seventeen chapters, the first part containing the exercises and the second part the solutions.
Author: César Polcino Milies Publisher: Springer ISBN: 9781402002397 Category : Mathematics Languages : en Pages : 0
Book Description
Group rings play a central role in the theory of representations of groups and are very interesting algebraic objects in their own right. In their study, many branches of algebra come to a rich interplay. This book takes the reader from beginning to research level and contains many topics that, so far, were only found in papers published in scientific journals and, whenever possible, offers new proofs of known results. It also includes many historical notes and some applications. Audience: This book will be of interest to mathematicians working in the area of group rings and it serves as an introduction of the subject to graduate students.
Author: Viet Dung Nguyen Publisher: American Mathematical Soc. ISBN: 0821843702 Category : Mathematics Languages : en Pages : 377
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: Carl Clifton Faith
Author: Carl Faith
Author: Carl Clifton Faith
Author: Michiel Hazewinkel
Author: Nathan Jacobson
Author: Stuart A. Steinberg
Author: Shimshon A. Amitsur
Author: A. Giambruno
Author: Grigore Calugareanu
Author: César Polcino Milies
Author: Viet Dung Nguyen