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Author : Jagannadham V. Pakala
Publisher :
ISBN 13 :
Total Pages : 78 pages
Book Rating : 4.:/5 (743 download)
Download or read book Commutative Torsion Theory written by Jagannadham V. Pakala and published by . This book was released on 1979 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Paul E. Bland
Publisher : Wiley-VCH
ISBN 13 :
Total Pages : 164 pages
Book Rating : 4.X/5 (4 download)
Download or read book Topics in Torsion Theory written by Paul E. Bland and published by Wiley-VCH. This book was released on 1998-11-30 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Torsion theory provides an umbrella under which many classical properties of rings and modules can be reformulated. The purpose of this book is to provide the reader with a quick introduction to torsion theory and to study selected properties of rings and modules in this setting. The material presented ranges from a torsion theoretical treatment of standard topics in ring and module theory to how previously untreated properties of rings and modules might be dealt with in this setting. The approach has been to develop the material so that classical results can be recovered by selecting an appropriate torsion theory. Simple modules, maximal submodules, the Jacobson radical and modules with chain conditions are investigated relative to a torsion theory. A relative form of Nakayama’s lemma is given and a generalized Hopkins-Levitzki theorem is established. Injective and projective concepts are studied and a generalized Baer’s condition for injective modules and a generalized Fuchs condition for quasi-injective modules are shown to hold. Flat modules and covers and hulls of modules are investigated and the concept of a relative (quasi-)projective cover is used to characterize those rings which are right perfect modulo their torsion ideal. Torsion free covers are also studied and results are given which generalize well known results on torsion free covers for modules (with usual torsion) over an integral domain. Finally, (semi-)primitive, (semi-)simple and (semi-)prime rings are investigated in a torsion theoretical setting and rings which are right primitive relative to a torsion theory are linked to a form of density which is reminiscent of Jacobson density for right primitive rings.
Author : Jonathan S. Golan
Publisher : Longman Scientific and Technical
ISBN 13 :
Total Pages : 680 pages
Book Rating : 4.3/5 (91 download)
Download or read book Torsion Theories written by Jonathan S. Golan and published by Longman Scientific and Technical. This book was released on 1986 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : P. J. Fleury
Publisher : Springer
ISBN 13 : 3540393714
Total Pages : 152 pages
Book Rating : 4.5/5 (43 download)
Download or read book Advances in Non-Commutative Ring Theory written by P. J. Fleury and published by Springer. This book was released on 2006-11-15 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Fanggui Wang
Publisher : Springer
ISBN 13 : 9811033374
Total Pages : 714 pages
Book Rating : 4.8/5 (11 download)
Download or read book Foundations of Commutative Rings and Their Modules written by Fanggui Wang and published by Springer. This book was released on 2017-01-06 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the basics and recent developments of commutative algebra. A glance at the contents of the first five chapters shows that the topics covered are ones that usually are included in any commutative algebra text. However, the contents of this book differ significantly from most commutative algebra texts: namely, its treatment of the Dedekind–Mertens formula, the (small) finitistic dimension of a ring, Gorenstein rings, valuation overrings and the valuative dimension, and Nagata rings. Going further, Chapter 6 presents w-modules over commutative rings as they can be most commonly used by torsion theory and multiplicative ideal theory. Chapter 7 deals with multiplicative ideal theory over integral domains. Chapter 8 collects various results of the pullbacks, especially Milnor squares and D+M constructions, which are probably the most important example-generating machines. In Chapter 9, coherent rings with finite weak global dimensions are probed, and the local ring of weak global dimension two is elaborated on by combining homological tricks and methods of star operation theory. Chapter 10 is devoted to the Grothendieck group of a commutative ring. In particular, the Bass–Quillen problem is discussed. Finally, Chapter 11 aims to introduce relative homological algebra, especially where the related concepts of integral domains which appear in classical ideal theory are defined and investigated by using the class of Gorenstein projective modules. Each section of the book is followed by a selection of exercises of varying degrees of difficulty. This book will appeal to a wide readership from graduate students to academic researchers who are interested in studying commutative algebra.
Author : Paul-Jean Cahen
Publisher : CRC Press
ISBN 13 : 1000946762
Total Pages : 489 pages
Book Rating : 4.0/5 (9 download)
Download or read book Commutative Ring Theory written by Paul-Jean Cahen and published by CRC Press. This book was released on 2023-06-14 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the proceedings of the Second International Conference on Commutative Ring Theory in Fes, Morocco. The text details developments in commutative algebra, highlighting the theory of rings and ideals. It explores commutative algebra's connections with and applications to topological algebra and algebraic geometry.
Author : David Dobbs
Publisher : CRC Press
ISBN 13 : 1000939634
Total Pages : 578 pages
Book Rating : 4.0/5 (9 download)
Download or read book Advances in Commutative Ring Theory written by David Dobbs and published by CRC Press. This book was released on 2023-08-25 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Presents the proceedings of the recently held Third International Conference on Commutative Ring Theory in Fez, Morocco. Details the latest developments in commutative algebra and related areas-featuring 26 original research articles and six survey articles on fundamental topics of current interest. Examines wide-ranging developments in commutative algebra, together with connections to algebraic number theory and algebraic geometry."
Author : Joachim Lambek
Publisher : Springer
ISBN 13 : 354036448X
Total Pages : 100 pages
Book Rating : 4.5/5 (43 download)
Download or read book Torsion Theories, Additive Semantics, and Rings of Quotients written by Joachim Lambek and published by Springer. This book was released on 2006-11-15 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: With an Appendix on Torsion Theories and Dominant Dimensions
Author : David Dobbs
Publisher : CRC Press
ISBN 13 : 1000945820
Total Pages : 574 pages
Book Rating : 4.0/5 (9 download)
Download or read book Advances in Commutative Ring Theory written by David Dobbs and published by CRC Press. This book was released on 2023-08-25 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Presents the proceedings of the recently held Third International Conference on Commutative Ring Theory in Fez, Morocco. Details the latest developments in commutative algebra and related areas-featuring 26 original research articles and six survey articles on fundamental topics of current interest. Examines wide-ranging developments in commutative algebra, together with connections to algebraic number theory and algebraic geometry."
Author : Jagannadham V. Pakala
Publisher :
ISBN 13 :
Total Pages : 156 pages
Book Rating : 4.:/5 (589 download)
Download or read book Commutative Torsion Theories written by Jagannadham V. Pakala and published by . This book was released on 1979 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Willy Brandal
Publisher :
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4.3/5 (91 download)
Download or read book Torsion Theories Over Commutative Rings written by Willy Brandal and published by . This book was released on 1996 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Commutative Torsion Theories written by and published by . This book was released on 1981 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Eben Matlis
Publisher : University of Chicago Press
ISBN 13 : 9780226510743
Total Pages : 180 pages
Book Rating : 4.5/5 (17 download)
Download or read book Torsion-Free Modules written by Eben Matlis and published by University of Chicago Press. This book was released on 1972 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of torsion-free modules over an arbitrary integral domain arises naturally as a generalization of torsion-free abelian groups. In this volume, Eben Matlis brings together his research on torsion-free modules that has appeared in a number of mathematical journals. Professor Matlis has reworked many of the proofs so that only an elementary knowledge of homological algebra and commutative ring theory is necessary for an understanding of the theory. The first eight chapters of the book are a general introduction to the theory of torsion-free modules. This part of the book is suitable for a self-contained basic course on the subject. More specialized problems of finding all integrally closed D-rings are examined in the last seven chapters, where material covered in the first eight chapters is applied. An integral domain is said to be a D-ring if every torsion-free module of finite rank decomposes into a direct sum of modules of rank 1. After much investigation, Professor Matlis found that an integrally closed domain is a D-ring if, and only if, it is the intersection of at most two maximal valuation rings.
Author : Fanggui Wang
Publisher : Springer Nature
ISBN 13 : 9819752841
Total Pages : 862 pages
Book Rating : 4.8/5 (197 download)
Download or read book Foundations of Commutative Rings and Their Modules written by Fanggui Wang and published by Springer Nature. This book was released on with total page 862 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Apostolos Beligiannis
Publisher : American Mathematical Soc.
ISBN 13 : 0821839969
Total Pages : 224 pages
Book Rating : 4.8/5 (218 download)
Download or read book Homological and Homotopical Aspects of Torsion Theories written by Apostolos Beligiannis and published by American Mathematical Soc.. This book was released on 2007 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors investigate homological and homotopical aspects of a concept of torsion which is general enough to cover torsion and cotorsion pairs in abelian categories, $t$-structures and recollements in triangulated categories, and torsion pairs in stable categories. The proper conceptual framework for this study is the general setting of pretriangulated categories, an omnipresent class of additive categories which includes abelian, triangulated, stable, and moregenerally (homotopy categories of) closed model categories in the sense of Quillen, as special cases. The main focus of their study is on the investigation of the strong connections and the interplay between (co)torsion pairs and tilting theory in abelian, triangulated and stable categories on one hand,and universal cohomology theories induced by torsion pairs on the other hand. These new universal cohomology theories provide a natural generalization of the Tate-Vogel (co)homology theory. The authors also study the connections between torsion theories and closed model structures, which allow them to classify all cotorsion pairs in an abelian category and all torsion pairs in a stable category, in homotopical terms. For instance they obtain a classification of (co)tilting modules along theselines. Finally they give torsion theoretic applications to the structure of Gorenstein and Cohen-Macaulay categories, which provide a natural generalization of Gorenstein and Cohen-Macaulay rings.
Author : V. K. A. M. Gugenheim
Publisher : American Mathematical Soc.
ISBN 13 : 0821818422
Total Pages : 107 pages
Book Rating : 4.8/5 (218 download)
Download or read book On the Theory and Applications of Differential Torsion Products written by V. K. A. M. Gugenheim and published by American Mathematical Soc.. This book was released on 1974 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approach to differential homological algebra is developed, one which exploits more general types of resolutions than the bicomplexes used traditionally. An example of such a generalized resolution is exhibited and is used to prove that the differential torsion product reduces to the classical torsion product in favorable cases. This result is used to compute the cohomology of various spaces. The paper also includes proofs (within the new framework) of the results of Eilenberg and Moore which relate differential torsion products to the homology and cohomology of spaces, and a discussion of the relationship between differential torsion products and matric Massey products.
Author : S.K. Jain
Publisher : Springer Science & Business Media
ISBN 13 : 1461219787
Total Pages : 330 pages
Book Rating : 4.4/5 (612 download)
Download or read book Advances in Ring Theory written by S.K. Jain and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:
