Injective Modules And Injective Quotient Rings
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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 .)
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 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.
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.
Report On Injective Modules
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Author : Chi-te Tsai
language : en
Publisher: Kingston, Ont : Queen's University, 1965 [c1966]
Release Date : 1965
Report On Injective Modules written by Chi-te Tsai and has been published by Kingston, Ont : Queen's University, 1965 [c1966] this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Algebraic fields categories.
Extending Modules
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Author : Nguyen Viet Dung
language : en
Publisher: Routledge
Release Date : 2019-01-22
Extending Modules written by Nguyen Viet Dung and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-22 with Mathematics categories.
Module theory is an important tool for many different branches of mathematics, as well as being an interesting subject in its own right. Within module theory, the concept of injective modules is particularly important. Extending modules form a natural class of modules which is more general than the class of injective modules but retains many of its
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.
Rings Of Quotients
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Author : B. Stenström
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Rings Of Quotients written by B. Stenström 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.
The theory of rings of quotients has its origin in the work of (j). Ore and K. Asano on the construction of the total ring of fractions, in the 1930's and 40's. But the subject did not really develop until the end of the 1950's, when a number of important papers appeared (by R. E. Johnson, Y. Utumi, A. W. Goldie, P. Gabriel, J. Lambek, and others). Since then the progress has been rapid, and the subject has by now attained a stage of maturity, where it is possible to make a systematic account of it (which is the purpose of this book). The most immediate example of a ring of quotients is the field of fractions Q of a commutative integral domain A. It may be characterized by the two properties: (i) For every qEQ there exists a non-zero SEA such that qSEA. (ii) Q is the maximal over-ring of A satisfying condition (i). The well-known construction of Q can be immediately extended to the case when A is an arbitrary commutative ring and S is a multiplicatively closed set of non-zero-divisors of A. In that case one defines the ring of fractions Q = A [S-l] as consisting of pairs (a, s) with aEA and SES, with the declaration that (a, s)=(b, t) if there exists UES such that uta = usb. The resulting ring Q satisfies (i), with the extra requirement that SES, and (ii).
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)