Matrices Over Commutative Rings
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Theory Of Generalized Inverses Over Commutative Rings
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Author : K.P.S. Bhaskara Rao
language : en
Publisher: CRC Press
Release Date : 2002-03-21
Theory Of Generalized Inverses Over Commutative Rings written by K.P.S. Bhaskara Rao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-03-21 with Mathematics categories.
The theory of generalized inverses of real or complex matrices has been expertly developed and documented. But the generalized inverses of matrices over rings have received comprehensive treatment only recently. In this book, the author, who contributed to the research and development of the theory, explains his results. He explores regular element
Matrices Over Commutative Rings
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Author : William Brown
language : en
Publisher: CRC Press
Release Date : 1992-11-23
Matrices Over Commutative Rings written by William Brown and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-11-23 with Mathematics categories.
Aims to cover the most important aspects of the theory of matrices whose entries come from a given commutative ring. Essential facts about commutative rings are developed throughout the book, and proofs that follow from concrete matrix calculations are also provided.
Linear Algebra Over Commutative Rings
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Author : Bernard R. McDonald
language : en
Publisher: CRC Press
Release Date : 2020-11-26
Linear Algebra Over Commutative Rings written by Bernard R. McDonald and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-26 with Mathematics categories.
This monograph arose from lectures at the University of Oklahoma on topics related to linear algebra over commutative rings. It provides an introduction of matrix theory over commutative rings. The monograph discusses the structure theory of a projective module.
Formal Matrices
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Author : Piotr Krylov
language : en
Publisher: Springer
Release Date : 2017-03-30
Formal Matrices written by Piotr Krylov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-30 with Mathematics categories.
This monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory. While various special types of formal matrix rings have been studied for a long time from several points of view and appear in various textbooks, for instance to examine equivalences of module categories and to illustrate rings with one-sided non-symmetric properties, this particular class of rings has, so far, not been treated systematically. Exploring formal matrix rings of order 2 and introducing the notion of the determinant of a formal matrix over a commutative ring, this monograph further covers the Grothendieck and Whitehead groups of rings. Graduate students and researchers interested in ring theory, module theory and operator algebras will find this book particularly valuable. Containing numerous examples, Formal Matrices is a largely self-contained and accessible introduction to the topic, assuming a solid understanding of basic algebra.
Finitely Generated Abelian Groups And Similarity Of Matrices Over A Field
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Author : Christopher Norman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-25
Finitely Generated Abelian Groups And Similarity Of Matrices Over A Field written by Christopher Norman 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 2012-01-25 with Mathematics categories.
At first sight, finitely generated abelian groups and canonical forms of matrices appear to have little in common. However, reduction to Smith normal form, named after its originator H.J.S.Smith in 1861, is a matrix version of the Euclidean algorithm and is exactly what the theory requires in both cases. Starting with matrices over the integers, Part 1 of this book provides a measured introduction to such groups: two finitely generated abelian groups are isomorphic if and only if their invariant factor sequences are identical. The analogous theory of matrix similarity over a field is then developed in Part 2 starting with matrices having polynomial entries: two matrices over a field are similar if and only if their rational canonical forms are equal. Under certain conditions each matrix is similar to a diagonal or nearly diagonal matrix, namely its Jordan form. The reader is assumed to be familiar with the elementary properties of rings and fields. Also a knowledge of abstract linear algebra including vector spaces, linear mappings, matrices, bases and dimension is essential, although much of the theory is covered in the text but from a more general standpoint: the role of vector spaces is widened to modules over commutative rings. Based on a lecture course taught by the author for nearly thirty years, the book emphasises algorithmic techniques and features numerous worked examples and exercises with solutions. The early chapters form an ideal second course in algebra for second and third year undergraduates. The later chapters, which cover closely related topics, e.g. field extensions, endomorphism rings, automorphism groups, and variants of the canonical forms, will appeal to more advanced students. The book is a bridge between linear and abstract algebra.
Linear Systems Over Commutative Rings
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Author : James W. Brewer
language : en
Publisher: CRC Press
Release Date : 1986-04-22
Linear Systems Over Commutative Rings written by James W. Brewer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-04-22 with Mathematics categories.
Separable Algebras Over Commutative Rings
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Author : Frank DeMeyer
language : en
Publisher: Springer
Release Date : 1971
Separable Algebras Over Commutative Rings written by Frank DeMeyer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Algebra categories.
These lecture notes were prepared by the authors for use in graduate courses and seminars, based on the work of many earlier mathematicians. In addition to very elementary results, presented for the convenience of the reader, Chapter I contains the Morita theorems and the definition of the projective class group of a commutative ring. Chapter II addresses the Brauer group of a commutative ring, and automorphisms of separable algebras. Chapter III surveys the principal theorems of the Galois theory for commutative rings. In Chapter IV the authors present a direct derivation of the first six terms of the seven-term exact sequence for Galois cohomology. In the fifth and final chapter the authors illustrate the preceding material with applications to the structure of central simple algebras and the Brauer group of a Dedekind domain, and they pose problems for further investigation. Exercises are included at the end of each chapter.
Theory Of Clean Rings And Matrices
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Author : Huanyin Chen
language : en
Publisher: World Scientific
Release Date : 2022-08-30
Theory Of Clean Rings And Matrices written by Huanyin Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-30 with Mathematics categories.
This is the first monograph devoted to clean ring and matrix theory. It aims to study a theory of expressing an element in a ring as the sum of some special ones, such as idempotents, units, nilpotents, tripotents, involutions, etc. A matrix over such rings is thereby expressed as the sum of some special matrices. Also another topics on the behaviors of topological properties and *-properties of such rings are investigated.The book is based on the results of various published papers, particularly, by the authors'. It is accessible for students familiar with general abstract algebra, while the topics are interesting for researchers in the field of ring, matrix and operator theory.
Computational Linear And Commutative Algebra
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Author : Martin Kreuzer
language : en
Publisher: Springer
Release Date : 2016-09-06
Computational Linear And Commutative Algebra written by Martin Kreuzer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-06 with Mathematics categories.
This book combines, in a novel and general way, an extensive development of the theory of families of commuting matrices with applications to zero-dimensional commutative rings, primary decompositions and polynomial system solving. It integrates the Linear Algebra of the Third Millennium, developed exclusively here, with classical algorithmic and algebraic techniques. Even the experienced reader will be pleasantly surprised to discover new and unexpected aspects in a variety of subjects including eigenvalues and eigenspaces of linear maps, joint eigenspaces of commuting families of endomorphisms, multiplication maps of zero-dimensional affine algebras, computation of primary decompositions and maximal ideals, and solution of polynomial systems. This book completes a trilogy initiated by the uncharacteristically witty books Computational Commutative Algebra 1 and 2 by the same authors. The material treated here is not available in book form, and much of it is not available at all. The authors continue to present it in their lively and humorous style, interspersing core content with funny quotations and tongue-in-cheek explanations.
On The Ring Of Matrices Commutative With A Given Matrix
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Author : Harold Callander Trimble
language : en
Publisher:
Release Date : 1939
On The Ring Of Matrices Commutative With A Given Matrix written by Harold Callander Trimble and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1939 with categories.