Methods In Module Theory
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Methods In Module Theory
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Author : Abrams
language : en
Publisher: CRC Press
Release Date : 1992-10-16
Methods In Module Theory written by Abrams and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-10-16 with Mathematics categories.
A collection of articles embodying the work presented at the 1991 Methods in Module Theory Conference at the University of Colorado at Colorado Springs - facilitating the explanation and cross-fertilization of new techniques that were developed to answer a variety of module-theoretic questions.
Almost Free Modules
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Author : P.C. Eklof
language : en
Publisher: Elsevier
Release Date : 1990-04-23
Almost Free Modules written by P.C. Eklof and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-04-23 with Mathematics categories.
This is an extended treatment of the set-theoretic techniques which have transformed the study of abelian group and module theory over the last 15 years. Part of the book is new work which does not appear elsewhere in any form. In addition, a large body of material which has appeared previously (in scattered and sometimes inaccessible journal articles) has been extensively reworked and in many cases given new and improved proofs. The set theory required is carefully developed with algebraists in mind, and the independence results are derived from explicitly stated axioms. The book contains exercises and a guide to the literature and is suitable for use in graduate courses or seminars, as well as being of interest to researchers in algebra and logic.
Foundations Of Module And Ring Theory
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Author : Robert Wisbauer
language : en
Publisher: Routledge
Release Date : 2018-05-11
Foundations Of Module And Ring Theory written by Robert Wisbauer and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-11 with Mathematics categories.
This volume provides a comprehensive introduction to module theory and the related part of ring theory, including original results as well as the most recent work. It is a useful and stimulating study for those new to the subject as well as for researchers and serves as a reference volume. Starting form a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. For a module M, the smallest Grothendieck category containing it is denoted by o[M] and module theory is developed in this category. Developing the techniques in o[M] is no more complicated than in full module categories and the higher generality yields significant advantages: for example, module theory may be developed for rings without units and also for non-associative rings. Numerous exercises are included in this volume to give further insight into the topics covered and to draw attention to related results in the literature.
Commutative Algebra Constructive Methods
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Author : Henri Lombardi
language : en
Publisher: Springer
Release Date : 2015-07-22
Commutative Algebra Constructive Methods written by Henri Lombardi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-22 with Mathematics categories.
Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra. It takes a constructive viewpoint in commutative algebra and studies algorithmic approaches alongside several abstract classical theories. Indeed, it revisits these traditional topics with a new and simplifying manner, making the subject both accessible and innovative. The algorithmic aspects of such naturally abstract topics as Galois theory, Dedekind rings, Prüfer rings, finitely generated projective modules, dimension theory of commutative rings, and others in the current treatise, are all analysed in the spirit of the great developers of constructive algebra in the nineteenth century. This updated and revised edition contains over 350 well-arranged exercises, together with their helpful hints for solution. A basic knowledge of linear algebra, group theory, elementary number theory as well as the fundamentals of ring and module theory is required. Commutative Algebra: Constructive Methods will be useful for graduate students, and also researchers, instructors and theoretical computer scientists.
Modular Representation Theory
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Author : D. Benson
language : en
Publisher: Springer
Release Date : 2008-07-22
Modular Representation Theory written by D. Benson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-22 with Mathematics categories.
This reprint of a 1983 Yale graduate course makes results in modular representation theory accessible to an audience ranging from second-year graduate students to established mathematicians. Following a review of background material, the lectures examine three closely connected topics in modular representation theory of finite groups: representations rings; almost split sequences and the Auslander-Reiten quiver; and complexity and cohomology varieties, which has become a major theme in representation theory.
Rings Of Quotients
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Author : B. Stenström
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Rings Of Quotients written by B. Stenström and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The theory of rings of quotients has its origin in the work of (j). Ore and K. Asano on the construction of the total ring of fractions, in the 1930's and 40's. But the subject did not really develop until the end of the 1950's, when a number of important papers appeared (by R. E. Johnson, Y. Utumi, A. W. Goldie, P. Gabriel, J. Lambek, and others). Since then the progress has been rapid, and the subject has by now attained a stage of maturity, where it is possible to make a systematic account of it (which is the purpose of this book). The most immediate example of a ring of quotients is the field of fractions Q of a commutative integral domain A. It may be characterized by the two properties: (i) For every qEQ there exists a non-zero SEA such that qSEA. (ii) Q is the maximal over-ring of A satisfying condition (i). The well-known construction of Q can be immediately extended to the case when A is an arbitrary commutative ring and S is a multiplicatively closed set of non-zero-divisors of A. In that case one defines the ring of fractions Q = A [S-l] as consisting of pairs (a, s) with aEA and SES, with the declaration that (a, s)=(b, t) if there exists UES such that uta = usb. The resulting ring Q satisfies (i), with the extra requirement that SES, and (ii).
Methods In Ring Theory
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Author : Freddy Van Oystaeyen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Methods In Ring Theory written by Freddy Van Oystaeyen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Proceedings of the NATO Advanced Study Institute, Antwerp, Belgium, August 2-12, 1983
Modules And The Structure Of Rings
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Author : Golan
language : en
Publisher: CRC Press
Release Date : 2017-10-19
Modules And The Structure Of Rings written by Golan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
This textbook is designed for students with at least one solid semester of abstract algebra,some linear algebra background, and no previous knowledge of module theory. Modulesand the Structure of Rings details the use of modules over a ring as a means of consideringthe structure of the ring itself--explaining the mathematics and "inductivereasoning" used in working on ring theory challenges and emphasizing modules insteadof rings.Stressing the inductive aspect of mathematical research underlying the formal deductivestyle of the literature, this volume offers vital background on current methods for solvinghard classification problems of algebraic structures. Written in an informal butcompletely rigorous style, Modules and the Structure of Rings clarifies sophisticatedproofs ... avoids the formalism of category theory ... aids independent study or seminarwork ... and supplies end-of-chapter problems.This book serves as an excellent primary.text for upper-level undergraduate and graduatestudents in one-semester courses on ring or module theory-laying a foundation formore advanced study of homological algebra or module theory.
A First Course In Module Theory
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Author : M. E. Keating
language : en
Publisher: World Scientific Publishing Company
Release Date : 1998-01-01
A First Course In Module Theory written by M. E. Keating and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.
An introduction to module theory for students with some knowledge of linear algebra and elementary ring theory. Expounds the basics of module theory, including methods of comparing, constructing and decomposing modules, then presents the structure theory of modules over Euclidean domains. Concluding chapters look at two standard forms for a square matrix, and projective modules over rings in general. Annotation copyrighted by Book News, Inc., Portland, OR
Modules And The Structure Of Rings
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Author : Golan
language : en
Publisher: CRC Press
Release Date : 1991-04-24
Modules And The Structure Of Rings written by Golan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-04-24 with Mathematics categories.
This book offers vital background information on methods for solving hard classification problems of algebraic structures. It explains how algebraists deal with the problem of the structure of modules over rings and how they make use of these structures to classify rings.