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Wednesday, August 5, 2020 | History

4 edition of Rings and categories of modules found in the catalog.

Rings and categories of modules

by Anderson, Frank W.

  • 76 Want to read
  • 12 Currently reading

Published by Springer-Verlag in New York .
Written in English

    Subjects:
  • Modules (Algebra),
  • Rings (Algebra),
  • Categories (Mathematics)

  • Edition Notes

    StatementFrank W. Anderson, Kent R. Fuller.
    SeriesGraduate texts in mathematics ;, 13
    ContributionsFuller, Kent R., joint author.
    Classifications
    LC ClassificationsQA247 .A55
    The Physical Object
    Paginationviii, 339 p. ;
    Number of Pages339
    ID Numbers
    Open LibraryOL5109118M
    ISBN 100387900691, 0387900705
    LC Control Number74181596

    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. Our general approach is categorical rather than arithmetical. . : 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 : Hardcover.

    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. Stanford Libraries' official online search tool for books, media, journals, databases, government documents and more.

    The category of rings is, therefore, isomorphic to the category Z-Alg. Many statements about the category of rings can be generalized to statements about the category of R-algebras. For each commutative ring R there is a functor R-Alg → Ring which forgets the R-module structure. 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.


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Rings and categories of modules by Anderson, Frank W. 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 standard undergraduate algebra courses. Our general approach Rings and categories of modules book categorical rather Cited by: 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 by: 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. Our general approach is categorical rather than arithmetical. 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. 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 Brand: Springer-Verlag Berlin Heidelberg. 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. Our general approach is categorical rather than arithmetical. Rings and Categories of Modules book. Read reviews from world’s largest community for readers.

This book is intended to provide a reasonably self-contain /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 standard undergraduate algebra 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, 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. 8. Semisimple Modules and Homological Dimension.- 9. Noetherian Semiprime Rings.- Orders in Semilocal Matrix Rings.- III Tensor Algebra.- Tensor Products and Flat Modules.- Morita Theorems and the Picard Group.- Algebras over Fields.- IV Structure of Abelian Categories.- Grothendieck Categories.- Quotient Categories and Brand: Springer Berlin Heidelberg.

Waldhausen categories and algebraic K-theory 2. Cylinders, homotopies, and approximation theorems 3. Application to categories of R-modules 4. Homotopy invariance and Quillen’s algebraic K-theory of rings 5. Morita equivalence 6. Multiplicative structure in the commutative case 7.

The plus construction description File Size: 1MB. Bibliography, v. 1, p. () v. 2, p. () v. Rings, modules, and categoriesv. Ring theoryPages: Foundations of Module and Ring Theory A Handbook for Study and Research Robert Wisbauer 37 Regular modules and rings. 38 Copure sequences and derived notions.

Chapter 8 Modules described by means of projectivity covered in the book. Categories of the type σ[M] are the starting point for a. Rings and Categories of Modules (Graduate Texts in Mathematics) by is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules.

Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of /5(7). 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.4/5(2).

I am reading the book Rings and Categories of Modules by Anderson and Fuller. I don't understand corollary $$ of that book. Can anyone explain that. In algebra, given a ring R, the category of left modules over R is the category whose objects are all left modules over R and whose morphisms are all module homomorphisms between left example, when R is the ring of integers Z, it is the same thing as the category of abelian category of right modules is defined in a similar way.

Note: Some authors. Algebra: Rings, Modules and Categories I 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. I think one needs to see the real world in order to understand software modules. Shipyards and railyards with their standard freight containers, standard gauge offer.

It is assumed that R and S are rings and R m and S m are the categories of all left R-modules and left S-modules, respectively. An (R, S) adjoint triple is a triple of additive functors. It is shown that a triple of functors (G, F, H) is an (R, S) adjoint triple if there is bimodule gPR with PR finitely generated and projective such that.Abelian Groups, Rings, Modules, and Homological Algebra (Lecture Notes in Pure and Applied Mathematics series) by Pat Goeters.

About the book In honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work.Rings Fileds Books.

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.