Rings Close To Regular

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Rings Close To Regular

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Author : A.A. Tuganbaev
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Rings Close To Regular written by A.A. Tuganbaev 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 2013-03-09 with Mathematics categories.

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.

Canadian Mathematical Bulletin

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Author :
language : en
Publisher:
Release Date : 1975

Canadian Mathematical Bulletin written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.

Smarandache Near Rings

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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date : 2002

Smarandache Near Rings written by W. B. Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B in A which is embedded with a stronger structure S. These types of structures occur in our everyday life, that's why we study them in this book. Thus, as a particular case: A Near-Ring is a non-empty set N together with two binary operations '+' and '.' such that (N, +) is a group (not necessarily abelian), (N, .) is a semigroup. For all a, b, c in N we have (a + b) . c = a . c + b . c. A Near-Field is a non-empty set P together with two binary operations '+' and '.' such that (P, +) is a group (not necessarily abelian), (P \ {0}, .) is a group. For all a, b, c I P we have (a + b) . c = a . c + b . c. A Smarandache Near-ring is a near-ring N which has a proper subset P in N, where P is a near-field (with respect to the same binary operations on N).

Near Rings And Near Fields

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Author : Yuen Fong
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Near Rings And Near Fields written by Yuen Fong 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 2012-12-06 with Mathematics categories.

Near-Rings and Near-Fields opens with three invited lectures on different aspects of the history of near-ring theory. These are followed by 26 papers reflecting the diversity of the subject in regard to geometry, topological groups, automata, coding theory and probability, as well as the purely algebraic structure theory of near-rings. Audience: Graduate students of mathematics and algebraists interested in near-ring theory.

Characterization Of Weak Bi Ideals In Bi Near Rings

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Author : S. Maharasi
language : en
Publisher: Infinite Study
Release Date :

Characterization Of Weak Bi Ideals In Bi Near Rings written by S. Maharasi and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

In this paper, with a new idea, we define weak bi-ideal and investigate some of its properties. We characterize weak bi-ideal by biideals of bi-near ing .In the case of left selfdistributive S-bi-near ring We establish necessary and sufficient condition for weak bi-ideal to be bi-ideal and strong bi-ideal.This concept motivates the study of different kinds of new biregular bi-near rings in algebraic theory especially regularity in quad near ring and fuzzy logic.

The Theory Of Near Rings

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Author : Robert Lockhart
language : en
Publisher: Springer Nature
Release Date : 2021-11-14

The Theory Of Near Rings written by Robert Lockhart and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-14 with Mathematics categories.

This book offers an original account of the theory of near-rings, with a considerable amount of material which has not previously been available in book form, some of it completely new. The book begins with an introduction to the subject and goes on to consider the theory of near-fields, transformation near-rings and near-rings hosted by a group. The bulk of the chapter on near-fields has not previously been available in English. The transformation near-rings chapters considerably augment existing knowledge and the chapters on product hosting are essentially new. Other chapters contain original material on new classes of near-rings and non-abelian group cohomology. The Theory of Near-Rings will be of interest to researchers in the subject and, more broadly, ring and representation theorists. The presentation is elementary and self-contained, with the necessary background in group and ring theory available in standard references.

Radical Theory Of Rings

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Author : J.W. Gardner
language : en
Publisher: CRC Press
Release Date : 2003-11-19

Radical Theory Of Rings written by J.W. Gardner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-19 with Mathematics categories.

Radical Theory of Rings distills the most noteworthy present-day theoretical topics, gives a unified account of the classical structure theorems for rings, and deepens understanding of key aspects of ring theory via ring and radical constructions. Assimilating radical theory's evolution in the decades since the last major work on rings and radicals was published, the authors deal with some distinctive features of the radical theory of nonassociative rings, associative rings with involution, and near-rings. Written in clear algebraic terms by globally acknowledged authorities, the presentation includes more than 500 landmark and up-to-date references providing direction for further research.

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.

Canadian Journal Of Mathematics

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Author :
language : en
Publisher:
Release Date : 1970

Canadian Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with categories.

Rings Modules And Closure Operations

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Author : Jesse Elliott
language : en
Publisher: Springer Nature
Release Date : 2019-11-30

Rings Modules And Closure Operations written by Jesse Elliott and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-30 with Mathematics categories.

This book presents a systematic exposition of the various applications of closure operations in commutative and noncommutative algebra. In addition to further advancing multiplicative ideal theory, the book opens doors to the various uses of closure operations in the study of rings and modules, with emphasis on commutative rings and ideals. Several examples, counterexamples, and exercises further enrich the discussion and lend additional flexibility to the way in which the book is used, i.e., monograph or textbook for advanced topics courses.