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Wednesday, July 29, 2020 | History

6 edition of Rings and Categories of Modules (Graduate Texts in Mathematics) found in the catalog.

# Rings and Categories of Modules (Graduate Texts in Mathematics)

## by Frank W. Anderson

Written in English

The Physical Object
Number of Pages392
ID Numbers
Open LibraryOL7449551M
ISBN 100387978453
ISBN 109780387978451

"This book follows in the footsteps of the valuable work done during the seventies of systematizing the investigation of properties and structure of rings by using their categories of modules. A remarkable novelty in the present monograph is the study of semiperfect rings by means of quivers. Author: Michiel Hazewinkel, Nadiya Gubareni, V.V. Kirichenko. Modules over the Polynomial Ring F[x] Deﬂned by a Linear Map Direct Sums of Submodules 1 Rings The Deﬂnition of a Ring We have been working with ﬂelds, which are the natural generalization of familiar objects like the real, rational and complex numbers where it is possible to add, subtract, multiply and.

: Algebra: Rings, modules and categories (Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, No. ) () by Faith, Carl Clifton and a great selection of similar New, Used and Collectible Books available now at great prices. Rings and Categories of Modules的书评 (全部 1 条) 热门 / 最新 / 好友 Greg 科学出版社版.

CONTENTS 3 Constructions of 1-Operads Subcategories of O-Monoidal 1-Categories. The papers are related to noncommutative rings, covering topics such as: ring theory, with both the elementwise and more structural approaches developed; module theory with popular topics such as automorphism invariance, almost injectivity, ADS, and extending modules; and coding theory, both the theoretical aspects such as the extension theorem.

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### Rings and Categories of Modules (Graduate Texts in Mathematics) by Frank W. Anderson Download PDF EPUB FB2

This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil- iarity with rings usually acquired in /5. This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses.

We assume the famil­ iarity with rings usually acquired in Cited by: Rings and Categories of Modules Frank W.

Anderson, Kent R. Fuller This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses.

VI of Oregon lectures inBass gave simplified proofs of a number of "Morita Theorems", incorporating ideas of Chase and Schanuel. One of the Morita theorems characterizes when there is an equivalence of categories mod-A R::. mod-B for two rings A and B. Morita's solution organizes ideas so efficiently that the classical Wedderburn-Artin theorem is a simple consequence, and moreover, a Brand: Springer-Verlag Berlin Heidelberg.

Introduction This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings Rings and Categories of Modules book modules suitable as a text for introductory and more advanced graduate courses.

We assume the famil­ iarity with rings usually acquired in standard undergraduate algebra courses. Rings, modules and homomorphisms --Direct sums and products --Finiteness conditions for modules --Classical ring-structure theorems --Functions between module categories --Equivalence and duality for module categories --Injective modules, projective modules, and their decompositions --Classical artinian rings.

Series Title. This classic monograph is geared toward advanced undergraduates and graduate students. The treatment presupposes some familiarity with sets, groups, rings, and vector spaces. The four-part approach begins with examinations of sets and maps, monoids and groups, categories, and rings.

The second part explores unique factorization domains, general module theory, semisimple rings and modules, and Artinian : Maurice Auslander, David Buchsbaum. Bibliography, v. 1, p. () v. 2, p.

() v. Rings, modules, and categoriesv. Ring theory. On the one hand this book intends to provide an introduction to module theory and the related part of ring theory. Topics covered includes: Elementary properties of rings, Module categories, Modules characterized by the Hom-functor, Notions derived from simple modules, Finiteness conditions in modules, Dual finiteness conditions, Pure sequences and derived notions, Relations between functors and Functor rings.

(c) If $\phi:R\to R$ is both a module homomorphism and a ring homomorphism, what can we say about $\phi$. Read solution Click here if solved 18 Add to solve later. Rings and Categories of Modules. Usually dispatched within 3 to 5 business days. Usually dispatched within 3 to 5 business days.

This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. This book is intended to provide a self-contained account of much of the theory of rings and modules.

The theme of the text throughout is the relationship between the one-sided ideal structure a ring may possess and the behavior of its categories of modules.

Rings and Categories of Modules - Frank W. Anderson, Kent R. Fuller - Google Books. This book is intended to provide a reasonably self-contained account of. Rings and categories of modules. New York: Springer-Verlag, [] (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: Frank W Anderson; Kent R Fuller.

Exercise 4. Express the notion of morphism of R-modules in the language of Exercise 1. Remark Suppose that Mis an S-module, and: R!Sis a map of rings. Then M is also naturally an R-module, via the action rm:= (r) m. This is often called the restriction of M along. In particular, any ring map R!Smakes the regular S-module SSinto an R-module.

Rings and modules Notation: AˆB means Ais a subset of B, possibly equal to B. Revision All rings are commutative rings with unity. Let f:A!B be a ring homomorphism. Theorem on ring homomorphisms. The kernel I of f is an ideal of A, the image C of f is a subring of B.

The quotient ring A=I is isomorphic to C. modules over a graded ring form categories of the type σ[M]. For orientation, at the beginning of every section the titles of the para- graphs occurring in it are listed.

At the end of the sections exercises are. In mathematics, specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship between quotients, homomorphisms, and ns of the theorems exist for groups, rings, vector spaces, modules, Lie algebras, and various other algebraic universal algebra, the isomorphism theorems can be.

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 book serves as an excellent for upper-level undergraduate and graduatestudents in.

Chapter II. Structured ring and module spectra 35 1. The category of S-modules 35 2. The mirror image to the category of S-modules 39 3. S-algebras and their modules 41 4. Free A∞ and E∞ ring spectra and comparisons of deﬁnitions 44 5. Free modules over A∞ and E∞ ring spectra 47 6.

Composites of monads and monadic tensor products 50 7. 8. Simple and Semisimple rings and Modules 66 Simple and Semisimple rings 66 Injective Modules 67 Simple and Semisimple Modules 70 Noetherian Modules 73 9. Radical and Socle 76 Localization 81 Local rings 81 Localization 81 Monoidal Categories 87 Bialgebras and Hopf Algebras 92 Bialgebras 92   Description This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses.

We assume the famil iarity with rings usually acquired in standard undergraduate algebra courses/5(7).Foundations of Module and Ring Theory book.

By Robert Wisbauer. Edition 1st Edition. First Published eBook Published 11 May Pub eBook ISBN Subjects Mathematics & Statistics. Back to book. chapter 2.

69 Pages. Module categories. By Wisbauer Robert. 1. Modules. 2. Submodules. 3. Rings without unit. 4.