Author : Piotr A. Krylov
Publisher : Walter de Gruyter
Page : 376 pages
File Size : 12,20 MB
Release : 2008
Category : Mathematics
ISBN : 9783110200539
"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.
Author : Piotr A. Krylov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 338 pages
File Size : 49,84 MB
Release : 2018-09-24
Category : Mathematics
ISBN : 3110611147
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
Author : Piotr A. Krylov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 397 pages
File Size : 18,40 MB
Release : 2018-09-24
Category : Mathematics
ISBN : 3110609851
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
Author : Piotr A. Krylov
Publisher : Walter de Gruyter
Page : 369 pages
File Size : 35,99 MB
Release : 2008-08-27
Category : Mathematics
ISBN : 3110205785
This book provides the first systematic treatment of modules over discrete valuation domains which plays 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 which is supplemented by exercises and interesting open problems. An important contribution to commutative algebra.
Author : László Fuchs
Publisher : CRC Press
Page : 340 pages
File Size : 13,85 MB
Release : 1985-03-27
Category : Mathematics
ISBN : 9780824773267
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.
Author : Craig Huneke
Publisher : Cambridge University Press
Page : 446 pages
File Size : 37,52 MB
Release : 2006-10-12
Category : Mathematics
ISBN : 0521688604
Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Author : Irving Kaplansky
Publisher : Courier Dover Publications
Page : 113 pages
File Size : 34,10 MB
Release : 2018-12-19
Category : Mathematics
ISBN : 0486836452
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.
Author : David F. Anderson
Publisher : CRC Press
Page : 820 pages
File Size : 23,42 MB
Release : 1995-04-10
Category : Mathematics
ISBN : 9780824796051
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.
Author :
Publisher :
Page : 1026 pages
File Size : 28,73 MB
Release : 1983-12
Category : Mathematics
ISBN :
Author : Michael F. Atiyah
Publisher : CRC Press
Page : 140 pages
File Size : 29,16 MB
Release : 2018-03-09
Category : Mathematics
ISBN : 0429973268
First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.
