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.
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 .)
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.
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 Algebras, Linear 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 Associative rings 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.
Lectures On Modules And Rings
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Author : Tsit-Yuen Lam
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lectures On Modules And Rings written by Tsit-Yuen 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 2012-12-06 with Mathematics categories.
This new book can be read independently from the first volume and may be used for lecturing, seminar- and self-study, or for general reference. It focuses more on specific topics in order to introduce readers to a wealth of basic and useful ideas without the hindrance of heavy machinery or undue abstractions. User-friendly with its abundance of examples illustrating the theory at virtually every step, the volume contains a large number of carefully chosen exercises to provide newcomers with practice, while offering a rich additional source of information to experts. A direct approach is used in order to present the material in an efficient and economic way, thereby introducing readers to a considerable amount of interesting ring theory without being dragged through endless preparatory material.
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.
Lecture Notes On Local Rings
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Author : Birger Iversen
language : en
Publisher: World Scientific
Release Date : 2014-06-20
Lecture Notes On Local Rings written by Birger Iversen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-20 with Mathematics categories.
The content in Chapter 1–3 is a fairly standard one-semester course on local rings with the goal to reach the fact that a regular local ring is a unique factorization domain. The homological machinery is also supported by Cohen–Macaulay rings and depth. In Chapters 4–6 the methods of injective modules, Matlis duality and local cohomology are discussed. Chapters 7–9 are not so standard and introduce the reader to the generalizations of modules to complexes of modules. Some of Professor Iversen's results are given in Chapter 9. Chapter 10 is about Serre's intersection conjecture. The graded case is fully exposed. The last chapter introduces the reader to Fitting ideals and McRae invariants. Contents:Dimension of a Local RingModules over a Local RingDivisor TheoryCompletionInjective ModulesLocal CohomologyDualizing ComplexesLocal DualityAmplitude and DimensionIntersection MultiplicitiesComplexes of Free Modules Readership: Graduate students and academic researchers with an interest in algebra, commutative algebra, algebra geometry, homological algebra and algebraic number theory. Key Features:Although the proofs are fairly short, the key points give readers the opportunity to supply details for their own satisfactionThe classical result of Auslander-Buchsbaum on unique factorization in a regular local ring is treated in a context of divisor and Picard groups, and this enlightens and connects to methods from number theoryThis book contains original research of the late Professor Iversen that are not published in this form beforeKeywords:Local Rings;Injective Modules;Matlis Duality;Local Cohomology;Birger's Results;Serre's Intersection Conjecture;Fitting Ideals;McRae InvariantsReviews: “This is a very nice text on some important topics on commutative ring theory.” Mathematical Association of America
Introductory Lectures On Rings And Modules
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Author : John A. Beachy
language : en
Publisher: Cambridge University Press
Release Date : 1999-04-22
Introductory Lectures On Rings And Modules written by John A. Beachy 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 1999-04-22 with Mathematics categories.
A first-year graduate text or reference for advanced undergraduates on noncommutative aspects of rings and modules.