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.
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
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
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.
Module Theory
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Author : Alberto Facchini
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-06-16
Module Theory written by Alberto Facchini 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 1998-06-16 with Mathematics categories.
This expository monograph was written for three reasons. Firstly, we wanted to present the solution to a problem posed by Wolfgang Krull in 1932 [Krull 32]. He asked whether what we now call the "Krull-Schmidt Theorem" holds for ar tinian modules. The problem remained open for 63 years: its solution, a negative answer to Krull's question, was published only in 1995 (see [Facchini, Herbera, Levy and Vamos]). Secondly, we wanted to present the answer to a question posed by Warfield in 1975 [Warfield 75]. He proved that every finitely pre sented module over a serial ring is a direct sum of uniserial modules, and asked if such a decomposition was unique. In other words, Warfield asked whether the "Krull-Schmidt Theorem" holds for serial modules. The solution to this problem, a negative answer again, appeared in [Facchini 96]. Thirdly, the so lution to Warfield's problem shows interesting behavior, a rare phenomenon in the history of Krull-Schmidt type theorems. Essentially, the Krull-Schmidt Theorem holds for some classes of modules and not for others. When it does hold, any two indecomposable decompositions are uniquely determined up to a permutation, and when it does not hold for a class of modules, this is proved via an example. For serial modules the Krull-Schmidt Theorem does not hold, but any two indecomposable decompositions are uniquely determined up to two permutations. We wanted to present such a phenomenon to a wider math ematical audience.
Rings Modules Algebras And Abelian Groups
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Author : Alberto Facchini
language : en
Publisher: CRC Press
Release Date : 2020-02-10
Rings Modules Algebras And Abelian Groups written by Alberto Facchini and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-10 with Mathematics categories.
Rings, Modules, Algebras, and Abelian Groups summarizes the proceedings of a recent algebraic conference held at Venice International University in Italy. Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, module and ring theory, and topological
Foundations Of Module And Ring Theory
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Author : Robert Wisbauer
language : en
Publisher: CRC Press
Release Date : 1991-09-05
Foundations Of Module And Ring Theory written by Robert Wisbauer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-09-05 with Mathematics categories.
Translated (with the addition of a number of new results, exercises, and references) from the German original of 1988 (Verlag Reinhard Fischer, Munich), 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. Starting from a basic understanding of linear algebra, the theory is presented with complete proofs. For undergraduate, graduate, and research level mathematicians working in algebra, module, and ring theory. Annotation copyrighted by Book News, Inc., Portland, OR
Matrix Methods
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Author : Vadim Olshevsky
language : en
Publisher: World Scientific
Release Date : 2010
Matrix Methods written by Vadim Olshevsky and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
Matrix methods provide the key to many problems in pure and applied mathematics. However, linear algebra theory, numerical algorithms and matrices in FEM/BEM applications usually live as if in three separate worlds. In this volume, maybe for the first time ever, they are compiled together as one entity as it was at the Moscow meeting, where the algebraic part was impersonated by Hans Schneider, algorithms by Gene Golub, and applications by Guri Marchuk. All topics intervened in plenary sessions are specially categorized into three sections of this volume. --
Algebraic And Symbolic Computation Methods In Dynamical Systems
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Author : Alban Quadrat
language : en
Publisher: Springer Nature
Release Date : 2020-05-30
Algebraic And Symbolic Computation Methods In Dynamical Systems written by Alban Quadrat and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-30 with Science categories.
This book aims at reviewing recent progress in the direction of algebraic and symbolic computation methods for functional systems, e.g. ODE systems, differential time-delay equations, difference equations and integro-differential equations. In the nineties, modern algebraic theories were introduced in mathematical systems theory and in control theory. Combined with real algebraic geometry, which was previously introduced in control theory, the past years have seen a flourishing development of algebraic methods in control theory. One of the strengths of algebraic methods lies in their close connections to computations. The use of the above-mentioned algebraic theories in control theory has been an important source of motivation to develop effective versions of these theories (when possible). With the development of computer algebra and computer algebra systems, symbolic methods for control theory have been developed over the past years. The goal of this book is to propose a partial state of the art in this direction. To make recent results more easily accessible to a large audience, the chapters include materials which survey the main mathematical methods and results and which are illustrated with explicit examples.
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).