Lectures On Injective Modules And Quotient Rings

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Lectures On Injective Modules And Quotient Rings

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Author : Carl Faith
language : en
Publisher: Springer
Release Date : 2006-11-14

Lectures On Injective Modules And Quotient Rings written by Carl Faith and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Lectures On Injective Modules And Quotient Rings

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Author : Carl Clifton Faith
language : en
Publisher:
Release Date : 1967

Lectures On Injective Modules And Quotient Rings written by Carl Clifton Faith and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Injective modules (Algebra) categories.

Injective Modules And Injective Quotient Rings

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Author : Faith
language : en
Publisher: CRC Press
Release Date : 2019-08-21

Injective Modules And Injective Quotient Rings written by Faith and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-21 with Mathematics categories.

First published in 1982. These lectures are in two parts. Part I, entitled injective Modules Over Levitzki Rings, studies an injective module E and chain conditions on the set A^(E,R) of right ideals annihilated by subsets of E. Part II is on the subject of (F)PF, or (finitely) pseudo-Frobenius, rings [i.e., all (finitely generated) faithful modules generate the category mod-R of all R-modules]. (The PF rings had been introduced by Azumaya as a generalization of quasi-Frobenius rings, but FPF includes infinite products of Prufer domains, e.g., Z w .)

Injective Modules And Injective Quotient Rings

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Author : Carl Faith
language : en
Publisher: CRC Press
Release Date : 2019-08-21

Injective Modules And Injective Quotient Rings written by Carl Faith and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-21 with Mathematics categories.

First published in 1982. These lectures are in two parts. Part I, entitled injective Modules Over Levitzki Rings, studies an injective module E and chain conditions on the set A^(E,R) of right ideals annihilated by subsets of E. Part II is on the subject of (F)PF, or (finitely) pseudo-Frobenius, rings [i.e., all (finitely generated) faithful modules generate the category mod-R of all R-modules]. (The PF rings had been introduced by Azumaya as a generalization of quasi-Frobenius rings, but FPF includes infinite products of Prufer domains, e.g., Z w .)

Canadian Journal Of Mathematics

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Author :
language : en
Publisher:
Release Date : 1971-11

Canadian Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-11 with categories.

Lectures On Rings And Modules

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Author : Joachim Lambek
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

Lectures On Rings And Modules written by Joachim Lambek and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

This book is an introduction to the theory of associative rings and their modules, designed primarily for graduate students. The standard topics on the structure of rings are covered, with a particular emphasis on the concept of the complete ring of quotients. A survey of the fundamental concepts of algebras in the first chapter helps to make the treatment self-contained. The topics covered include selected results on Boolean and other commutative rings, the classical structure theory of associative rings, injective modules, and rings of quotients. The final chapter provides an introduction to homological algebra. Besides three appendices on further results, there is a six-page section of historical comments. Table of Contents: Fundamental Concepts of Algebra: 1.1 Rings and related algebraic systems; 1.2 Subrings, homomorphisms, ideals; 1.3 Modules, direct products, and direct sums; 1.4 Classical isomorphism theorems. Selected Topics on Commutative Rings: 2.1 Prime ideals in commutative rings; 2.2 Prime ideals in special commutative rings; 2.3 The complete ring of quotients of a commutative ring; 2.4 Rings of quotients of commutative semiprime rings; 2.5 Prime ideal spaces.Classical Theory of Associative Rings: 3.1 Primitive rings; 3.2 Radicals; 3.3 Completely reducible modules; 3.4 Completely reducible rings; 3.5 Artinian and Noetherian rings; 3.6 On lifting idempotents; 3.7 Local and semiperfect rings. Injectivity and Related Concepts: 4.1 Projective modules; 4.2 Injective modules; 4.3 The complete ring of quotients; 4.4 Rings of endomorphisms of injective modules; 4.5 Regular rings of quotients; 4.6 Classical rings of quotients; 4.7 The Faith-Utumi theorem. Introduction to Homological Algebra: 5.1 Tensor products of modules; 5.2 Hom and $\otimes$ as functors; 5.3 Exact sequences; 5.4 Flat modules; 5.5 Torsion and extension products. Appendixes; Comments; Bibliography; Index. Review from Zentralblatt Math: Due to their clarity and intelligible presentation, these lectures on rings and modules are a particularly successful introduction to the surrounding circle of ideas. Review from American Mathematical Monthly: An introduction to associative rings and modules which requires of the reader only the mathematical maturity which one would attain in a first-year graduate algebra [course]...in order to make the contents of the book as accessible as possible, the author develops all the fundamentals he will need.In addition to covering the basic topics...the author covers some topics not so readily available to the nonspecialist...the chapters are written to be as independent as possible...[which will be appreciated by] students making their first acquaintance with the subject...one of the most successful features of the book is that it can be read by graduate students with little or no help from a specialist. (CHEL/283.H)

Rings And Modules Of Quotients

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Author : B. Stenström
language : en
Publisher: Springer
Release Date : 2006-11-15

Rings And Modules Of Quotients written by B. Stenström and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Exercises In Modules And Rings

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Author : T.Y. Lam
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-12-15

Exercises In Modules And Rings written by T.Y. Lam 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 2006-12-15 with Mathematics categories.

This volume offers a compendium of exercises of varying degree of difficulty in the theory of modules and rings. It is the companion volume to GTM 189. All exercises are solved in full detail. Each section begins with an introduction giving the general background and the theoretical basis for the problems that follow.

Injective Modules And Injective Quotient Rings

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Author : Carl Faith
language : en
Publisher:
Release Date : 2019

Injective Modules And Injective Quotient Rings written by Carl Faith and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Injective modules (Algebra) categories.

First published in 1982. These lectures are in two parts. Part I, entitled injective Modules Over Levitzki Rings, studies an injective module E and chain conditions on the set A^(E, R) of right ideals annihilated by subsets of E. Part II is on the subject of (F)PF, or (finitely) pseudo-Frobenius, rings [i.e. all (finitely generated) faithful modules generate the category mod-R of all R-modules]. (The PF rings had been introduced by Azumaya as a generalization of quasi-Frobenius rings, but FPF includes infinite products of Prufer domains, e.g., Z w .)

Groups Rings And Algebras

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Author : Donald S. Passman
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Groups Rings And Algebras written by Donald S. Passman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

This is a companion volume to the conference in honor of Donald S. Passman held in Madison, Wisconsin in June 2005. It contains research papers on Algebras, Group Rings, Hopf Algebras, Invariant Theory, Lie Algebras and their Enveloping Algebras, Noncommutative Algebraic Geometry, Noncommutative Rings, and other topics. The papers represent an important part of the latest research in these areas.