Module Theory

Author : Thomas Scott Blyth
Publisher : Unknown
Page : 376 pages
File Size : 48,9 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015018842735

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Module Theory by Thomas Scott Blyth Pdf

This textbook provides a self-contained course on the basic properties of modules and their importance in the theory of linear algebra. The first 11 chapters introduce the central results and applications of the theory of modules. Subsequent chapters deal with advanced linear algebra, including multilinear and tensor algebra, and explore such topics as the exterior product approach to the determinants of matrices, a module-theoretic approach to the structure of finitely generated Abelian groups, canonical forms, and normal transformations. Suitable for undergraduate courses, the text now includes a proof of the celebrated Wedderburn-Artin theorem which determines the structure of simple Artinian rings.

Author : Alberto Facchini
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 53,7 Mb
Release : 2012-02-03
Category : Mathematics
ISBN : 9783034803038

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Module Theory by Alberto Facchini Pdf

This book presents topics in module theory and ring theory: some, such as Goldie dimension and semiperfect rings are now considered classical and others more specialized, such as dual Goldie dimension, semilocal endomorphism rings, serial rings and modules.

Author : Robert Wisbauer
Publisher : Routledge
Page : 425 pages
File Size : 47,8 Mb
Release : 2018-05-11
Category : Mathematics
ISBN : 9781351447348

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Foundations of Module and Ring Theory by Robert Wisbauer Pdf

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.

Author : William A. Adkins,Steven H. Weintraub
Publisher : Springer Science & Business Media
Page : 540 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209232

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Algebra by William A. Adkins,Steven H. Weintraub Pdf

This book is designed as a text for a first-year graduate algebra course. As necessary background we would consider a good undergraduate linear algebra course. An undergraduate abstract algebra course, while helpful, is not necessary (and so an adventurous undergraduate might learn some algebra from this book). Perhaps the principal distinguishing feature of this book is its point of view. Many textbooks tend to be encyclopedic. We have tried to write one that is thematic, with a consistent point of view. The theme, as indicated by our title, is that of modules (though our intention has not been to write a textbook purely on module theory). We begin with some group and ring theory, to set the stage, and then, in the heart of the book, develop module theory. Having developed it, we present some of its applications: canonical forms for linear transformations, bilinear forms, and group representations. Why modules? The answer is that they are a basic unifying concept in mathematics. The reader is probably already familiar with the basic role that vector spaces play in mathematics, and modules are a generaliza tion of vector spaces. (To be precise, modules are to rings as vector spaces are to fields.

Author : Alberto Facchini
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 43,7 Mb
Release : 2012-02-05
Category : Mathematics
ISBN : 9783034803021

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Module Theory by Alberto Facchini Pdf

This book presents topics in module theory and ring theory: some, such as Goldie dimension and semiperfect rings are now considered classical and others more specialized, such as dual Goldie dimension, semilocal endomorphism rings, serial rings and modules.

Author : C. Faith,S. Wiegand
Publisher : Springer
Page : 248 pages
File Size : 44,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540355380

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Module Theory by C. Faith,S. Wiegand Pdf

Author : Toma Albu,Gary F. Birkenmeier,Ali Erdogan,Adnan Tercan
Publisher : Springer Science & Business Media
Page : 200 pages
File Size : 45,6 Mb
Release : 2011-02-04
Category : Mathematics
ISBN : 9783034600071

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Ring and Module Theory by Toma Albu,Gary F. Birkenmeier,Ali Erdogan,Adnan Tercan Pdf

This book is a collection of invited papers and articles, many presented at the 2008 International Conference on Ring and Module Theory. The papers explore the latest in various areas of algebra, including ring theory, module theory and commutative algebra.

Author : Maurice Auslander,Mark Bridger
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 44,9 Mb
Release : 1969
Category : Commutative rings
ISBN : 9780821812945

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Stable Module Theory by Maurice Auslander,Mark Bridger Pdf

The notions of torsion and torsion freeness have played a very important role in module theory--particularly in the study of modules over integral domains. Furthermore, the use of homological techniques in this connection has been well established. It is the aim of this paper to extend these techniques and to show that this extension leads naturally to several new concepts (e.g. k-torsion freeness and Gorenstein dimension) which are useful in the classification of modules and rings.

Author : Adnan Tercan,Canan C. Yücel
Publisher : Birkhäuser
Page : 369 pages
File Size : 43,7 Mb
Release : 2016-05-13
Category : Mathematics
ISBN : 9783034809528

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Module Theory, Extending Modules and Generalizations by Adnan Tercan,Canan C. Yücel Pdf

The main focus of this monograph is to offer a comprehensive presentation of known and new results on various generalizations of CS-modules and CS-rings. Extending (or CS) modules are generalizations of injective (and also semisimple or uniform) modules. While the theory of CS-modules is well documented in monographs and textbooks, results on generalized forms of the CS property as well as dual notions are far less present in the literature. With their work the authors provide a solid background to module theory, accessible to anyone familiar with basic abstract algebra. The focus of the book is on direct sums of CS-modules and classes of modules related to CS-modules, such as relative (injective) ejective modules, (quasi) continuous modules, and lifting modules. In particular, matrix CS-rings are studied and clear proofs of fundamental decomposition results on CS-modules over commutative domains are given, thus complementing existing monographs in this area. Open problems round out the work and establish the basis for further developments in the field. The main text is complemented by a wealth of examples and exercises.

Author : Abrams
Publisher : CRC Press
Page : 352 pages
File Size : 46,9 Mb
Release : 1992-10-16
Category : Mathematics
ISBN : 0824788028

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Methods in Module Theory by Abrams Pdf

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.

Author : Mike E Keating
Publisher : World Scientific
Page : 271 pages
File Size : 42,6 Mb
Release : 1998-07-31
Category : Mathematics
ISBN : 9781783262403

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A First Course In Module Theory by Mike E Keating Pdf

This book is an introduction to module theory for the reader who knows something about linear algebra and ring theory. Its main aim is the derivation of the structure theory of modules over Euclidean domains. This theory is applied to obtain the structure of abelian groups and the rational canonical and Jordan normal forms of matrices. The basic facts about rings and modules are given in full generality, so that some further topics can be discussed, including projective modules and the connection between modules and representations of groups.The book is intended to serve as supplementary reading for the third or fourth year undergraduate who is taking a course in module theory. The further topics point the way to some projects that might be attempted in conjunction with a taught course.

Author : Lindsay N. Childs,Cornelius Greither,Kevin P. Keating,Alan Koch,Timothy Kohl,Paul J. Truman,Robert G. Underwood
Publisher : American Mathematical Soc.
Page : 311 pages
File Size : 49,5 Mb
Release : 2021-11-10
Category : Education
ISBN : 9781470465162

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Hopf Algebras and Galois Module Theory by Lindsay N. Childs,Cornelius Greither,Kevin P. Keating,Alan Koch,Timothy Kohl,Paul J. Truman,Robert G. Underwood Pdf

Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000. The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields. Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.

Author : Grigore Calugareanu
Publisher : Springer Science & Business Media
Page : 233 pages
File Size : 53,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401595889

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Lattice Concepts of Module Theory by Grigore Calugareanu Pdf

It became more and more usual, from, say, the 1970s, for each book on Module Theory, to point out and prove some (but in no more than 15 to 20 pages) generalizations to (mostly modular) lattices. This was justified by the nowadays widely accepted perception that the structure of a module over a ring is best understood in terms of the lattice struc ture of its submodule lattice. Citing Louis H. Rowen "this important example (the lattice of all the submodules of a module) is the raison d'etre for the study of lattice theory by ring theorists". Indeed, many module-theoretic results can be proved by using lattice theory alone. The purpose of this book is to collect and present all and only the results of this kind, although for this purpose one must develop some significant lattice theory. The results in this book are of the following categories: the folklore of Lattice Theory (to be found in each Lattice Theory book), module theoretic results generalized in (modular, and possibly compactly gen erated) lattices (to be found in some 6 to 7 books published in the last 20 years), very special module-theoretic results generalized in lattices (e. g. , purity in Chapter 9 and several dimensions in Chapter 13, to be found mostly in [27], respectively, [34] and [18]) and some new con cepts (e. g.

Author : Dikran Dikranjan,Luigi Salce
Publisher : CRC Press
Page : 381 pages
File Size : 44,5 Mb
Release : 2019-05-31
Category : Mathematics
ISBN : 9780429530067

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Abelian Groups, Module Theory, and Topology by Dikran Dikranjan,Luigi Salce Pdf

Features a stimulating selection of papers on abelian groups, commutative and noncommutative rings and their modules, and topological groups. Investigates currently popular topics such as Butler groups and almost completely decomposable groups.

Author : Lindsay Childs
Publisher : American Mathematical Soc.
Page : 225 pages
File Size : 43,9 Mb
Release : 2000
Category : Field extensions (Mathematics).
ISBN : 9780821821312

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Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory by Lindsay Childs Pdf

This book studies Hopf algebras over valuation rings of local fields and their application to the theory of wildly ramified extensions of local fields. The results, not previously published in book form, show that Hopf algebras play a natural role in local Galois module theory. Included in this work are expositions of short exact sequences of Hopf algebras; Hopf Galois structures on separable field extensions; a generalization of Noether's theorem on the Galois module structure of tamely ramified extensions of local fields to wild extensions acted on by Hopf algebras; connections between tameness and being Galois for algebras acted on by a Hopf algebra; constructions by Larson and Greither of Hopf orders over valuation rings; ramification criteria of Byott and Greither for the associated order of the valuation ring of an extension of local fields to be Hopf order; the Galois module structure of wildly ramified cyclic extensions of local fields of degree p and p2; and Kummer theory of formal groups. Beyond a general background in graduate-level algebra, some chapters assume an acquaintance with some algebraic number theory. From there, this exposition serves as an excellent resource and motivation for further work in the field.