[PDF] Distributive Modules And Related Topics eBook

Author : Askar Tuganbaev
Publisher : CRC Press
Page : 280 pages
File Size : 45,16 MB
Release : 1999-08-19
Category : Mathematics
ISBN : 9789056991920

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A comprehensive introduction to the homological and structural methods of ring theory and related topics, this book includes original results as well as the most recent work in the field. It is unique in that it concentrates on distributive modules and rings, an area in which the author is recognized as one of the world's leading experts. A module is said to be distributive if the lattice of its submodules is distributive. Distributive rings are exemplified by factor rings of direct products of division rings, commutative semihereditary rings, and uniserial rings. Direct sums of distributive modules are studied in detail, as well as relations with flat modules and modules whose endomorphisms could be extended or lifted. Starting from a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. A number of exercises are also included to give further insight into the topics covered and to draw attention to relevant results in the literature. This detailed and comprehensive book will be an invaluable source of reference to researchers and specialists in this area.

Author : Michiel Hazewinkel
Publisher : CRC Press
Page : 285 pages
File Size : 23,10 MB
Release : 2017-04-11
Category : Mathematics
ISBN : 1351869868

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The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This is the second volume of Algebras, Rings and Modules: Non-commutative Algebras and Rings by M. Hazewinkel and N. Gubarenis, a continuation stressing the more important recent results on advanced topics of the structural theory of associative algebras, rings and modules.

Author : P.A. Krylov
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 15,46 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 9401703450

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Every Abelian group can be related to an associative ring with an identity element, the ring of all its endomorphisms. Recently the theory of endomor phism rings of Abelian groups has become a rapidly developing area of algebra. On the one hand, it can be considered as a part of the theory of Abelian groups; on the other hand, the theory can be considered as a branch of the theory of endomorphism rings of modules and the representation theory of rings. There are several reasons for studying endomorphism rings of Abelian groups: first, it makes it possible to acquire additional information about Abelian groups themselves, to introduce new concepts and methods, and to find new interesting classes of groups; second, it stimulates further develop ment of the theory of modules and their endomorphism rings. The theory of endomorphism rings can also be useful for studies of the structure of additive groups of rings, E-modules, and homological properties of Abelian groups. The books of Baer [52] and Kaplansky [245] have played an important role in the early development of the theory of endomorphism rings of Abelian groups and modules. Endomorphism rings of Abelian groups are much stu died in monographs of Fuchs [170], [172], and [173]. Endomorphism rings are also studied in the works of Kurosh [287], Arnold [31], and Benabdallah [63].

Author : Piotr A. Krylov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 337 pages
File Size : 34,49 MB
Release : 2018-09-24
Category : Mathematics
ISBN : 3110611147

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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. ContentsPreliminariesBasic factsEndomorphism rings of divisible and complete modulesRepresentation of rings by endomorphism ringsTorsion-free modulesMixed modulesDeterminity of modules by their endomorphism ringsModules with many endomorphisms or automorphisms

Author :
Publisher : Springer Science & Business Media
Page : 266 pages
File Size : 20,9 MB
Release : 2003-03-31
Category : Mathematics
ISBN : 9781402012204

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The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.

Author : Y. Bahturin
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 11,97 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 1461302358

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The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.

Author : A. Giambruno
Publisher : American Mathematical Soc.
Page : 283 pages
File Size : 30,50 MB
Release : 2009
Category : Mathematics
ISBN : 0821847716

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Represents the proceedings of the conference on Groups, Rings and Group Rings, held July 28 - August 2, 2008, in Ubatuba, Brazil. This title contains results in active research areas in the theory of groups, group rings and algebras (including noncommutative rings), polynomial identities, Lie algebras and superalgebras.

Author : Piotr A. Krylov
Publisher : Walter de Gruyter
Page : 369 pages
File Size : 27,97 MB
Release : 2008-08-27
Category : Mathematics
ISBN : 3110205785

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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 :
Publisher : Elsevier
Page : 1185 pages
File Size : 33,2 MB
Release : 2003-10-15
Category : Mathematics
ISBN : 0080532977

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Handbook of Algebra

Author : A.A. Tuganbaev
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 27,45 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 9401598789

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Preface All rings are assumed to be associative and (except for nilrings and some stipulated cases) to have nonzero identity elements. A ring A is said to be regular if for every element a E A, there exists an element b E A with a = aba. Regular rings are well studied. For example, [163] and [350] are devoted to regular rings. A ring A is said to be tr-regular if for every element a E A, there is an element n b E A such that an = anba for some positive integer n. A ring A is said to be strongly tr-regular if for every a E A, there is a positive integer n with n 1 n an E a + An Aa +1. It is proved in [128] that A is a strongly tr-regular ring if and only if for every element a E A, there is a positive integer m with m 1 am E a + A. Every strongly tr-regular ring is tr-regular [38]. If F is a division ring and M is a right vector F-space with infinite basis {ei}~l' then End(MF) is a regular (and tr-regular) ring that is not strongly tr-regular. The factor ring of the ring of integers with respect to the ideal generated by the integer 4 is a strongly tr-regular ring that is not regular.