Rings That are Nearly Associative

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Publisher : Academic Press
ISBN 13 : 0080874231
Total Pages : 385 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Rings That are Nearly Associative by :

Download or read book Rings That are Nearly Associative written by and published by Academic Press. This book was released on 1982-10-07 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rings That are Nearly Associative

Rings that are Nearly Associative

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Publisher :
ISBN 13 : 9780127798509
Total Pages : 371 pages
Book Rating : 4.7/5 (985 download)

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Book Synopsis Rings that are Nearly Associative by : Konstantin Aleksandrovich Zhevlakov

Download or read book Rings that are Nearly Associative written by Konstantin Aleksandrovich Zhevlakov and published by . This book was released on 1982 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Rings and Things and a Fine Array of Twentieth Century Associative Algebra

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Publisher : American Mathematical Soc.
ISBN 13 : 0821836722
Total Pages : 513 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Rings and Things and a Fine Array of Twentieth Century Associative Algebra by : Carl Clifton Faith

Download or read book Rings and Things and a Fine Array of Twentieth Century Associative Algebra written by Carl Clifton Faith and published by American Mathematical Soc.. This book was released on 2004 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys more than 125 years of aspects of associative algebras, especially ring and module theory. It is the first to probe so extensively such a wealth of historical development. Moreover, the author brings the reader up to date, in particular through his report on the subject in the second half of the twentieth century. Included in the book are certain categorical properties from theorems of Frobenius and Stickelberger on the primary decomposition of finite Abelian formulations of the latter by Krull, Goldman, and others; Maschke's theorem on the representation theory of finite groups over a field; and the fundamental theorems of Wedderburn on the structure of finite dimensional algebras Goldie, and others. A special feature of the book is the in-depth study of rings with chain condition on annihilator ideals pioneered by Noether, Artin, and Jacobson and refined and extended by many later mathematicians. Two of the author's prior works, Algebra: Rings, Modules and Categories, I and II (Springer-Verlag, 1973), are devoted to the development of modern associative algebra and ring and module theory. Those bibliography of over 1,600 references and is exhaustively indexed. In addition to the mathematical survey, the author gives candid and descriptive impressions of the last half of the twentieth century in ''Part II: Snapshots of fellow graduate students at the University of Kentucky and at Purdue, Faith discusses his Fulbright-Nato Postdoctoral at Heidelberg and at the Institute for Advanced Study (IAS) at Princeton, his year as a visiting scholar at Berkeley, and the many acquaintances he met there and in subsequent travels in India, Europe, and most recently, Barcelona. Comments on the first edition: ''Researchers in algebra should find it both full references as to the origin and development of the theorem ... I know of no other work in print which does this as thoroughly and as broadly.'' --John O'Neill, University of Detroit at Mercy '' 'Part II: Snapshots of Mathematicians of my age and younger will relish reading 'Snapshots'.'' --James A. Huckaba, University of Missouri-Columbia

Rings Close to Regular

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Publisher : Springer Science & Business Media
ISBN 13 : 9401598789
Total Pages : 363 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Rings Close to Regular by : A.A. Tuganbaev

Download or read book Rings Close to Regular written by A.A. Tuganbaev and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Cogroups and Co-rings in Categories of Associative Rings

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Publisher : American Mathematical Soc.
ISBN 13 : 0821804952
Total Pages : 400 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Cogroups and Co-rings in Categories of Associative Rings by : George M. Bergman

Download or read book Cogroups and Co-rings in Categories of Associative Rings written by George M. Bergman and published by American Mathematical Soc.. This book was released on 1996 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies representable functors among well-known varieties of algebras. All such functors from associative rings over a fixed ring R to each of the categories of abelian groups, associative rings, Lie rings, and to several others are determined. Results are also obtained on representable functors on varieties of groups, semigroups, commutative rings, and Lie algebras. The book includes a "Symbol index", which serves as a glossary of symbols used and a list of the pages where the topics so symbolized are treated, and a "Word and phrase index". The authors have strived -- and succeeded -- in creating a volume that is very user-friendly.

Fixed Rings of Finite Automorphism Groups of Associative Rings

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Publisher : Springer
ISBN 13 : 3540383085
Total Pages : 133 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Fixed Rings of Finite Automorphism Groups of Associative Rings by : S. Montgomery

Download or read book Fixed Rings of Finite Automorphism Groups of Associative Rings written by S. Montgomery and published by Springer. This book was released on 2006-11-15 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Selected Works of A.I. Shirshov

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Publisher : Springer Science & Business Media
ISBN 13 : 3764388587
Total Pages : 235 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Selected Works of A.I. Shirshov by : Leonid A. Bokut

Download or read book Selected Works of A.I. Shirshov written by Leonid A. Bokut and published by Springer Science & Business Media. This book was released on 2009-11-09 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Anatolii Illarionovich Shirshov (1921–1981) was an outstanding Russian mat- maticianwhoseworksessentiallyin?uenced thetheoriesofassociative,Lie,Jordan and alternative rings. Many Shirshov’s students and students of his students had a successful research career in mathematics. AnatoliiShirshovwasbornonthe8thofAugustof1921inthevillageKolyvan near Novosibirsk. Before the II World War he started to study mathematics at Tomsk university but then went to the front to ?ght as a volunteer. In 1946 he continued his study at Voroshilovgrad (now Lugansk) Pedagogical Institute and at the same time taught mathematics at a secondary school. In 1950 Shirshov was accepted as a graduate student at the Moscow State University under the supervision of A. G. Kurosh. In 1953 he has successfully defended his Candidate of Science thesis (analog of a Ph. D. ) “Some problems in the theory of nonassociative rings and algebras” and joined the Department of Higher Algebra at the Moscow State University. In 1958 Shirshov was awarded the Doctor of Science degree for the thesis “On some classes of rings that are nearly associative”. In 1960 Shirshov moved to Novosibirsk (at the invitations of S. L. Sobolev and A. I. Malcev) to become one of the founders of the new mathematical institute of the Academy of Sciences (now Sobolev Institute of Mathematics) and to help the formation of the new Novosibirsk State University. From 1960 to 1973 he was a deputy director of the Institute and till his last days he led the research in the theory of algebras at the Institute.

Smarandache Near-Rings

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Publisher : Infinite Study
ISBN 13 : 1931233667
Total Pages : 201 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Smarandache Near-Rings by : W. B. Vasantha Kandasamy

Download or read book Smarandache Near-Rings written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2002 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Smarandache Non-Associative Rings

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Publisher : Infinite Study
ISBN 13 : 1931233691
Total Pages : 151 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Smarandache Non-Associative Rings by : W. B. Vasantha Kandasamy

Download or read book Smarandache Non-Associative Rings written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2002 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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's life, that's why we study them in this book. Thus, as a particular case: A Non-associative ring is a non-empty set R together with two binary operations '+' and '.' such that (R, +) is an additive abelian group and (R, .) is a groupoid. For all a, b, c in R we have (a + b) . c = a . c + b . c and c . (a + b) = c . a + c . b. A Smarandache non-associative ring is a non-associative ring (R, +, .) which has a proper subset P in R, that is an associative ring (with respect to the same binary operations on R).

Radical Theory of Rings

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Publisher : CRC Press
ISBN 13 : 9780203913352
Total Pages : 412 pages
Book Rating : 4.9/5 (133 download)

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Book Synopsis Radical Theory of Rings by : J.W. Gardner

Download or read book Radical Theory of Rings written by J.W. Gardner and published by CRC Press. This book was released on 2003-11-19 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Alternative Loop Rings

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Publisher : Elsevier
ISBN 13 : 008052706X
Total Pages : 404 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Alternative Loop Rings by : E.G. Goodaire

Download or read book Alternative Loop Rings written by E.G. Goodaire and published by Elsevier. This book was released on 1996-10-24 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the past ten years, alternative loop rings have intrigued mathematicians from a wide cross-section of modern algebra. As a consequence, the theory of alternative loop rings has grown tremendously.One of the main developments is the complete characterization of loops which have an alternative but not associative, loop ring. Furthermore, there is a very close relationship between the algebraic structures of loop rings and of group rings over 2-groups.Another major topic of research is the study of the unit loop of the integral loop ring. Here the interaction between loop rings and group rings is of immense interest.This is the first survey of the theory of alternative loop rings and related issues. Due to the strong interaction between loop rings and certain group rings, many results on group rings have been included, some of which are published for the first time. The authors often provide a new viewpoint and novel, elementary proofs in cases where results are already known.The authors assume only that the reader is familiar with basic ring-theoretic and group-theoretic concepts. They present a work which is very much self-contained. It is thus a valuable reference to the student as well as the research mathematician. An extensive bibliography of references which are either directly relevant to the text or which offer supplementary material of interest, are also included.

Automorphisms and Derivations of Associative Rings

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Publisher : Springer Science & Business Media
ISBN 13 : 9401136041
Total Pages : 398 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Automorphisms and Derivations of Associative Rings by : V. Kharchenko

Download or read book Automorphisms and Derivations of Associative Rings written by V. Kharchenko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebras, Rings and Modules

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Publisher : CRC Press
ISBN 13 : 1482245051
Total Pages : 384 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Algebras, Rings and Modules by : Michiel Hazewinkel

Download or read book Algebras, Rings and Modules written by Michiel Hazewinkel and published by CRC Press. This book was released on 2016-04-05 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 centu

Polynomial Identity Rings

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Publisher : Birkhäuser
ISBN 13 : 3034879342
Total Pages : 197 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Polynomial Identity Rings by : Vesselin Drensky

Download or read book Polynomial Identity Rings written by Vesselin Drensky and published by Birkhäuser. This book was released on 2012-12-06 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes treat polynomial identity rings from both the combinatorial and structural points of view. The greater part of recent research in polynomial identity rings is about combinatorial questions, and the combinatorial part of the lecture notes gives an up-to-date account of recent research. On the other hand, the main structural results have been known for some time, and the emphasis there is on a presentation accessible to newcomers to the subject.

On Certain Classes of Associative Rings

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Publisher :
ISBN 13 :
Total Pages : 3 pages
Book Rating : 4.:/5 (439 download)

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Book Synopsis On Certain Classes of Associative Rings by : A. R. Blass

Download or read book On Certain Classes of Associative Rings written by A. R. Blass and published by . This book was released on 1971 with total page 3 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Theory of Near-Rings

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Publisher : Springer Nature
ISBN 13 : 3030817555
Total Pages : 555 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis The Theory of Near-Rings by : Robert Lockhart

Download or read book The Theory of Near-Rings written by Robert Lockhart and published by Springer Nature. This book was released on 2021-11-14 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on Rings and Modules

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Publisher :
ISBN 13 :
Total Pages : 206 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Lectures on Rings and Modules by : Joachim Lambek

Download or read book Lectures on Rings and Modules written by Joachim Lambek and published by . This book was released on 1966 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: