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Modules Over Valuation Rings
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Book Synopsis Modules over Valuation Rings by : László Fuchs
Download or read book Modules over Valuation Rings written by László Fuchs and published by CRC Press. This book was released on 1985-03-27 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book initiates a systematic, in-depth study of Modules Over Valuation Domains. It introduces the theory of modules over commutative domains without finiteness conditions and examines frontiers of current research in modules over valuation domains. It represents a unique effort to combine ideas from abelian group theory, in a large scale, with powerful techniques developed in module theory. This volume surveys the background material on valuation rings, modules and homological algebra ... features new results for important classes of modules such as finitely generated, divisible, pure-injective, and projective dimension one -- never published before ... contains exercises and research problems -- offering guidance for independent and creative study ... and provides historical notes, comments, and an extensive bibliography. Mathematicians and advanced graduate-level mathematics students interested in module theory, abelian group theory, and commutative ring theory can stay abreast of the latest advances with Modules Over Valuation Domains. Book jacket.
Book Synopsis Modules Over Discrete Valuation Domains by : Piotr A. Krylov
Download or read book Modules Over Discrete Valuation Domains written by Piotr A. Krylov and published by Walter de Gruyter. This book was released on 2008 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In this book, modules over a specific class of rings, the discrete valuations domains, are considered. Such modules call for a special consideration, since they have specific properties and play an important role in various areas of algebra, especially of commutative algebra. The text is accompanied by exercises, historical remarks, links to related fields and open problems. It is useful for students, graduates studying algebra, young researchers, and experts."--BOOK JACKET.
Book Synopsis Modules over Discrete Valuation Rings by : Piotr A. Krylov
Download or read book Modules over Discrete Valuation Rings written by Piotr A. Krylov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-09-24 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first systematic treatment of modules over discrete valuation domains, which play an important role in various areas of algebra, especially in commutative algebra. Many important results representing the state of the art are presented in the text along with interesting open problems. This updated edition presents new approaches on p-adic integers and modules, and on the determinability of a module by its automorphism group. Contents Preliminaries Basic facts Endomorphism rings of divisible and complete modules Representation of rings by endomorphism rings Torsion-free modules Mixed modules Determinity of modules by their endomorphism rings Modules with many endomorphisms or automorphisms
Book Synopsis Integral Closure of Ideals, Rings, and Modules by : Craig Huneke
Download or read book Integral Closure of Ideals, Rings, and Modules written by Craig Huneke and published by Cambridge University Press. This book was released on 2006-10-12 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Book Synopsis Selected Papers and Other Writings by : Irving Kaplansky
Download or read book Selected Papers and Other Writings written by Irving Kaplansky and published by Springer Science & Business Media. This book was released on 1995-04-13 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is not often that one gets to write a preface to a collection of one's own papers. The most urgent task is to thank the people who made this book possible. That means first of all Hy Bass who, on behalf of Springer-Verlag, approached me about the idea. The late Walter Kaufmann-Biihler was very encouraging; Paulo Ribenboim helped in an important way; and Ina Lindemann saw the project through with tact and skill that I deeply appreciate. My wishes have been indulged in two ways. First, I was allowed to follow up each selected paper with an afterthought. Back in my student days I became aware of the Gesammelte Mathematische Werke of Dedekind, edited by Fricke, Noether, and Ore. I was impressed by the editors' notes that followed most of the papers and found them very usefuL A more direct model was furnished by the collected papers of Lars Ahlfors, in which the author himself supplied afterthoughts for each paper or group of papers. These were tough acts to follow, but I hope that some readers will find at least some of my afterthoughts interesting. Second, I was permitted to add eight previously unpublished items. My model here, to a certain extent, was the charming little book, A Mathematician's Miscel lany by J. E. Littlewood. In picking these eight I had quite a selection to make -from fourteen loose-leaf notebooks of such writings. Here again I hope that at least some will be found to be of interest.
Book Synopsis Modules over Non-Noetherian Domains by : László Fuchs
Download or read book Modules over Non-Noetherian Domains written by László Fuchs and published by American Mathematical Soc.. This book was released on 2001 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors present both traditional and modern discoveries in the subject area, concentrating on advanced aspects of the topic. Existing material is studied in detail, including finitely generated modules, projective and injective modules, and the theory of torsion and torsion-free modules. Some topics are treated from a new point of view. Also included are areas not found in current texts, for example, pure-injectivity, divisible modules, uniserial modules, etc. Special emphasis is given to results that are valid over arbitrary domains. The authors concentrate on modules over valuation and Prüfer domains, but also discuss Krull and Matlis domains, h-local, reflexive, and coherent domains. The volume can serve as a standard reference book for specialists working in the area and also is a suitable text for advanced-graduate algebra courses and seminars.
Book Synopsis Rings, Polynomials, and Modules by : Marco Fontana
Download or read book Rings, Polynomials, and Modules written by Marco Fontana and published by Springer. This book was released on 2017-11-11 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of articles highlighting recent developments in commutative algebra and related non-commutative generalizations. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non-Noetherian ring theory, module theory and integer-valued polynomials along with connections to algebraic number theory, algebraic geometry, topology and homological algebra. Most of the eighteen contributions are authored by attendees of the two conferences in commutative algebra that were held in the summer of 2016: “Recent Advances in Commutative Ring and Module Theory,” Bressanone, Italy; “Conference on Rings and Polynomials” Graz, Austria. There is also a small collection of invited articles authored by experts in the area who could not attend either of the conferences. Following the model of the talks given at these conferences, the volume contains a number of comprehensive survey papers along with related research articles featuring recent results that have not yet been published elsewhere.
Book Synopsis Advances in Algebra and Model Theory by : M Droste
Download or read book Advances in Algebra and Model Theory written by M Droste and published by CRC Press. This book was released on 2019-08-16 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains 25 surveys in algebra and model theory, all written by leading experts in the field. The surveys are based around talks given at conferences held in Essen, 1994, and Dresden, 1995. Each contribution is written in such a way as to highlight the ideas that were discussed at the conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community. The topics include field and ring theory as well as groups, ordered algebraic structure and their relationship to model theory. Several papers deal with infinite permutation groups, abelian groups, modules and their relatives and representations. Model theoretic aspects include quantifier elimination in skew fields, Hilbert's 17th problem, (aleph-0)-categorical structures and Boolean algebras. Moreover symmetry questions and automorphism groups of orders are covered. This work contains 25 surveys in algebra and model theory, each is written in such a way as to highlight the ideas that were discussed at Conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community.
Book Synopsis Abelian Groups, Module Theory, and Topology by : Dikran Dikranjan
Download or read book Abelian Groups, Module Theory, and Topology written by Dikran Dikranjan and published by CRC Press. This book was released on 2019-05-16 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features a stimulating selection of papers on abelian groups, commutative and noncommutative rings and their modules, and topological groups. Investigates currently popular topics such as Butler groups and almost completely decomposable groups.
Book Synopsis Semilocal Categories and Modules with Semilocal Endomorphism Rings by : Alberto Facchini
Download or read book Semilocal Categories and Modules with Semilocal Endomorphism Rings written by Alberto Facchini and published by Springer Nature. This book was released on 2019-10-23 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects and coherently presents the research that has been undertaken since the author’s previous book Module Theory (1998). In addition to some of the key results since 1995, it also discusses the development of much of the supporting material. In the twenty years following the publication of the Camps-Dicks theorem, the work of Facchini, Herbera, Shamsuddin, Puninski, Prihoda and others has established the study of serial modules and modules with semilocal endomorphism rings as one of the promising directions for module-theoretic research. Providing readers with insights into the directions in which the research in this field is moving, as well as a better understanding of how it interacts with other research areas, the book appeals to undergraduates and graduate students as well as researchers interested in algebra.
Download or read book Handbook of Algebra written by and published by Elsevier. This book was released on 2003-10-15 with total page 1185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Algebra
Book Synopsis Non-Commutative Valuation Rings and Semi-Hereditary Orders by : H. Marubayashi
Download or read book Non-Commutative Valuation Rings and Semi-Hereditary Orders written by H. Marubayashi and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Much progress has been made during the last decade on the subjects of non commutative valuation rings, and of semi-hereditary and Priifer orders in a simple Artinian ring which are considered, in a sense, as global theories of non-commu tative valuation rings. So it is worth to present a survey of the subjects in a self-contained way, which is the purpose of this book. Historically non-commutative valuation rings of division rings were first treat ed systematically in Schilling's Book [Sc], which are nowadays called invariant valuation rings, though invariant valuation rings can be traced back to Hasse's work in [Has]. Since then, various attempts have been made to study the ideal theory of orders in finite dimensional algebras over fields and to describe the Brauer groups of fields by usage of "valuations", "places", "preplaces", "value functions" and "pseudoplaces". In 1984, N. 1. Dubrovin defined non-commutative valuation rings of simple Artinian rings with notion of places in the category of simple Artinian rings and obtained significant results on non-commutative valuation rings (named Dubrovin valuation rings after him) which signify that these rings may be the correct def inition of valuation rings of simple Artinian rings. Dubrovin valuation rings of central simple algebras over fields are, however, not necessarily to be integral over their centers.
Download or read book Abelian Group Theory written by D. Arnold and published by Springer. This book was released on 2006-11-15 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Module Theory written by Alberto Facchini and published by Springer Science & Business Media. This book was released on 2012-02-05 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents topics in module theory and ring theory: some, such as Goldie dimension and semiperfect rings are now considered classical and others more specialized, such as dual Goldie dimension, semilocal endomorphism rings, serial rings and modules.
Book Synopsis Foundations of Module and Ring Theory by : Robert Wisbauer
Download or read book Foundations of Module and Ring Theory written by Robert Wisbauer and published by Routledge. This book was released on 2018-05-11 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive introduction to module theory and the related part of ring theory, including original results as well as the most recent work. It is a useful and stimulating study for those new to the subject as well as for researchers and serves as a reference volume. Starting form a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. For a module M, the smallest Grothendieck category containing it is denoted by o[M] and module theory is developed in this category. Developing the techniques in o[M] is no more complicated than in full module categories and the higher generality yields significant advantages: for example, module theory may be developed for rings without units and also for non-associative rings. Numerous exercises are included in this volume to give further insight into the topics covered and to draw attention to related results in the literature.
Book Synopsis Foundations of Commutative Rings and Their Modules by : Fanggui Wang
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.
Book Synopsis Commutative Ring Theory by : Paul-Jean Cahen
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 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: " Exploring commutative algebra's connections with and applications to topological algebra and algebraic geometry, Commutative Ring Theory covers the spectra of rings chain conditions, dimension theory, and Jaffard rings fiber products group rings, semigroup rings, and graded rings class groups linear groups integer-valued polynomials rings of finite fractions big Cohen-Macaulay modules and much more!"
