Modules Over Discrete Valuation Rings

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Modules Over Discrete Valuation Rings

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Author : Piotr A. Krylov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-09-24

Modules Over Discrete Valuation Rings written by Piotr A. Krylov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-24 with Mathematics categories.

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

Modules Over Discrete Valuation Domains

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Author : Piotr A. Krylov
language : en
Publisher: Walter de Gruyter
Release Date : 2008

Modules Over Discrete Valuation Domains written by Piotr A. Krylov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

"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.

Modules Over Discrete Valuation Rings

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Author : Piotr A. Krylov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-09-24

Modules Over Discrete Valuation Rings written by Piotr A. Krylov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-24 with Mathematics categories.

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

A Classification Of Modules Over Discrete Valuation Rings

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Author : Sharon Cutler Ross
language : en
Publisher:
Release Date : 1976

A Classification Of Modules Over Discrete Valuation Rings written by Sharon Cutler Ross and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Modules (Algebra) categories.

Modules Over Valuation Rings

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Author : László Fuchs
language : en
Publisher: CRC Press
Release Date : 1985-03-27

Modules Over Valuation Rings written by László Fuchs and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-03-27 with Mathematics categories.

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.

Integral Closure Of Ideals Rings And Modules

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Author : Craig Huneke
language : en
Publisher: Cambridge University Press
Release Date : 2006-10-12

Integral Closure Of Ideals Rings And Modules written by Craig Huneke 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 2006-10-12 with Mathematics categories.

Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.

Infinite Abelian Groups

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Author : Irving Kaplansky
language : en
Publisher: Courier Dover Publications
Release Date : 2018-12-19

Infinite Abelian Groups written by Irving Kaplansky and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-19 with Mathematics categories.

In the Introduction to this concise monograph, the author states his two main goals: first, "to make the theory of infinite abelian groups available in a convenient form to the mathematical public; second, to help students acquire some of the techniques used in modern infinite algebra." Suitable for advanced undergraduates and graduate students in mathematics, the text requires no extensive background beyond the rudiments of group theory. Starting with examples of abelian groups, the treatment explores torsion groups, Zorn's lemma, divisible groups, pure subgroups, groups of bounded order, and direct sums of cyclic groups. Subsequent chapters examine Ulm's theorem, modules and linear transformations, Banach spaces, valuation rings, torsion-free and complete modules, algebraic compactness, characteristic submodules, and the ring of endomorphisms. Many exercises appear throughout the book, along with a guide to the literature and a detailed bibliography.

Algebraic Geometry

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Author : Robin Hartshorne
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Algebraic Geometry written by Robin Hartshorne 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 2013-06-29 with Mathematics categories.

Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. After receiving his Ph.D. from Princeton in 1963, Hartshorne became a Junior Fellow at Harvard, then taught there for several years. In 1972 he moved to California where he is now Professor at the University of California at Berkeley. He is the author of "Residues and Duality" (1966), "Foundations of Projective Geometry (1968), "Ample Subvarieties of Algebraic Varieties" (1970), and numerous research titles. His current research interest is the geometry of projective varieties and vector bundles. He has been a visiting professor at the College de France and at Kyoto University, where he gave lectures in French and in Japanese, respectively. Professor Hartshorne is married to Edie Churchill, educator and psychotherapist, and has two sons. He has travelled widely, speaks several foreign languages, and is an experienced mountain climber. He is also an accomplished amateur musician: he has played the flute for many years, and during his last visit to Kyoto he began studying the shakuhachi.

Zero Dimensional Commutative Rings

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Author : David F. Anderson
language : en
Publisher: CRC Press
Release Date : 1995-04-10

Zero Dimensional Commutative Rings written by David F. Anderson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-04-10 with Mathematics categories.

This work presents advances in zero-dimensional commutative rings and commutative algebra. It illustrates the research frontier with 52 open problems together with comments on the relevant literature, and offers a comprehensive index for easy access to information. Wide-ranging developments in commutative ring theory are examined.

Deformations Of Nilpotent Matrices Over Rings And Reduction Of Analytic Families Of Meromorphic Differential Equations

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Author : Donald G. Babbitt
language : en
Publisher: American Mathematical Soc.
Release Date : 1985

Deformations Of Nilpotent Matrices Over Rings And Reduction Of Analytic Families Of Meromorphic Differential Equations written by Donald G. Babbitt 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 1985 with Mathematics categories.

This paper studies the reduction theory of analytic parametric families of systems of linear meromorphic differential equations in the neighborhood of an irregular singularity.