Modules Linear Endomorphisms And Algebras
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Modules Linear Endomorphisms And Algebras
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Author : Yutze Chow
language : en
Publisher: Gordon & Breach Science Publishers
Release Date : 1976
Modules Linear Endomorphisms And Algebras written by Yutze Chow and has been published by Gordon & Breach Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
Modern Abstract Algebra
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Author : Y. S. Chow
language : en
Publisher:
Release Date : 1976
Modern Abstract Algebra written by Y. S. Chow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Algebra, Abstract categories.
Modern Abstract Algebra Modules Linear Endomorphisms And Algebras
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Author : Yutze Chow
language : en
Publisher:
Release Date : 1976
Modern Abstract Algebra Modules Linear Endomorphisms And Algebras written by Yutze Chow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Algebra, Abstract categories.
Advanced Linear Algebra With An Introduction To Module Theory
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Author : Shou-te Chang
language : en
Publisher: World Scientific
Release Date : 2024-01-24
Advanced Linear Algebra With An Introduction To Module Theory written by Shou-te Chang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-24 with Mathematics categories.
Certain essential concepts in linear algebra cannot be fully explained in a first course. This is due to a lack of algebraic background for most beginning students. On the other hand, these concepts are taken for granted in most of the mathematical courses at graduate school level. This book will provide a gentle guidance for motivated students to fill the gap. It is not easy to find other books fulfilling this purpose. This book is a suitable textbook for a higher undergraduate course, as well as for a graduate student's self-study. The introduction of set theory and modules would be of particular interest to students who aspire to becoming algebraists.There are three parts to this book. One is to complete the discussion of bases and dimension in linear algebra. In a first course, only the finite dimensional vector spaces are treated, and in most textbooks, it will assume the scalar field is the real number field. In this book, the general case of arbitrary dimension and arbitrary scalar fields is examined. To do so, an introduction to cardinality and Zorn's lemma in set theory is presented in detail. The second part is to complete the proof of canonical forms for linear endomorphisms and matrices. For this, a generalization of vector spaces, and the most fundamental results regarding modules are introduced to readers. This will provide the natural entrance into a full understanding of matrices. Finally, tensor products of vector spaces and modules are briefly discussed.
Approximations And Endomorphism Algebras Of Modules
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Author : Rüdiger Göbel
language : en
Publisher: Walter de Gruyter
Release Date : 2012-10-01
Approximations And Endomorphism Algebras Of Modules written by Rüdiger Göbel and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-01 with Mathematics categories.
This second, revised and substantially extended edition of Approximations and Endomorphism Algebras of Modules reflects both the depth and the width of recent developments in the area since the first edition appeared in 2006. The new division of the monograph into two volumes roughly corresponds to its two central topics, approximation theory (Volume 1) and realization theorems for modules (Volume 2). It is a widely accepted fact that the category of all modules over a general associative ring is too complex to admit classification. Unless the ring is of finite representation type we must limit attempts at classification to some restricted subcategories of modules. The wild character of the category of all modules, or of one of its subcategories C, is often indicated by the presence of a realization theorem, that is, by the fact that any reasonable algebra is isomorphic to the endomorphism algebra of a module from C. This results in the existence of pathological direct sum decompositions, and these are generally viewed as obstacles to classification. In order to overcome this problem, the approximation theory of modules has been developed. The idea here is to select suitable subcategories C whose modules can be classified, and then to approximate arbitrary modules by those from C. These approximations are neither unique nor functorial in general, but there is a rich supply available appropriate to the requirements of various particular applications. The authors bring the two theories together. The first volume, Approximations, sets the scene in Part I by introducing the main classes of modules relevant here: the S-complete, pure-injective, Mittag-Leffler, and slender modules. Parts II and III of the first volume develop the key methods of approximation theory. Some of the recent applications to the structure of modules are also presented here, notably for tilting, cotilting, Baer, and Mittag-Leffler modules. In the second volume, Predictions, further basic instruments are introduced: the prediction principles, and their applications to proving realization theorems. Moreover, tools are developed there for answering problems motivated in algebraic topology. The authors concentrate on the impossibility of classification for modules over general rings. The wild character of many categories C of modules is documented here by the realization theorems that represent critical R-algebras over commutative rings R as endomorphism algebras of modules from C. The monograph starts from basic facts and gradually develops the theory towards its present frontiers. It is suitable both for graduate students interested in algebra and for experts in module and representation theory.
Module Theory
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Author : Thomas Scott Blyth
language : en
Publisher:
Release Date : 1990
Module Theory written by Thomas Scott Blyth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
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.
Modules And Rings
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Author : John Dauns
language : en
Publisher: Cambridge University Press
Release Date : 1994-10-28
Modules And Rings written by John Dauns and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-10-28 with Mathematics categories.
This book on modern module and non-commutative ring theory is ideal for beginning graduate students. It starts at the foundations of the subject and progresses rapidly through the basic concepts to help the reader reach current research frontiers. Students will have the chance to develop proofs, solve problems, and to find interesting questions. The first half of the book is concerned with free, projective, and injective modules, tensor algebras, simple modules and primitive rings, the Jacobson radical, and subdirect products. Later in the book, more advanced topics, such as hereditary rings, categories and functors, flat modules, and purity are introduced. These later chapters will also prove a useful reference for researchers in non-commutative ring theory. Enough background material (including detailed proofs) is supplied to give the student a firm grounding in the subject.
Finite Dimensional Algebras
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Author : Yurj A. Drozd
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Finite Dimensional Algebras written by Yurj A. Drozd 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.
This English edition has an additional chapter "Elements of Homological Al gebra". Homological methods appear to be effective in many problems in the theory of algebras; we hope their inclusion makes this book more complete and self-contained as a textbook. We have also taken this occasion to correct several inaccuracies and errors in the original Russian edition. We should like to express our gratitude to V. Dlab who has not only metic ulously translated the text, but has also contributed by writing an Appendix devoted to a new important class of algebras, viz. quasi-hereditary algebras. Finally, we are indebted to the publishers, Springer-Verlag, for enabling this book to reach such a wide audience in the world of mathematical community. Kiev, February 1993 Yu.A. Drozd V.V. Kirichenko Preface The theory of finite dimensional algebras is one of the oldest branches of modern algebra. Its origin is linked to the work of Hamilton who discovered the famous algebra of quaternions, and Cayley who developed matrix theory. Later finite dimensional algebras were studied by a large number of mathematicians including B. Peirce, C.S. Peirce, Clifford, ·Weierstrass, Dedekind, Jordan and Frobenius. At the end of the last century T. Molien and E. Cartan described the semisimple algebras over the complex and real fields and paved the first steps towards the study of non-semi simple algebras.
Lectures On Sl 2 C Modules
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Author : Mazorchuk Volodymyr
language : en
Publisher: World Scientific Publishing Company
Release Date : 2009-12-04
Lectures On Sl 2 C Modules written by Mazorchuk Volodymyr 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 2009-12-04 with Mathematics categories.
This book is directed primarily at undergraduate and postgraduate students interested to get acquainted with the representation theory of Lie algebras. The book treats the case of the smallest simple Lie algebra, namely, the Lie algebra sl_2. It contains classical contents including the description of all finite-dimensional modules and an introduction to the universal enveloping algebras with its primitive ideals, alongside non-classical contents including the description of all simple weight modules, the category of all weight modules, a detailed description of the category O, and especially, a description of all simple modules. The book also contains an account of a new research direction: the categorification of simple finite-dimensional modules./a
Rings Modules And Linear Algebra
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Author : Brian Hartley
language : en
Publisher: Taylor & Francis
Release Date : 1974
Rings Modules And Linear Algebra written by Brian Hartley and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.
