Near-rings: The Theory and its Applications PDF Download

Author:
Publisher: Elsevier
ISBN: 0080871348
Category : Mathematics
Languages : en
Pages : 487

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Near-rings: The Theory and its Applications

Author: Bhavanari Satyanarayana
Publisher: CRC Press
ISBN: 1439873100
Category : Computers
Languages : en
Pages : 482

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Book Description
Near Rings, Fuzzy Ideals, and Graph Theory explores the relationship between near rings and fuzzy sets and between near rings and graph theory. It covers topics from recent literature along with several characterizations. After introducing all of the necessary fundamentals of algebraic systems, the book presents the essentials of near rings theory, relevant examples, notations, and simple theorems. It then describes the prime ideal concept in near rings, takes a rigorous approach to the dimension theory of N-groups, gives some detailed proofs of matrix near rings, and discusses the gamma near ring, which is a generalization of both gamma rings and near rings. The authors also provide an introduction to fuzzy algebraic systems, particularly the fuzzy ideals of near rings and gamma near rings. The final chapter explains important concepts in graph theory, including directed hypercubes, dimension, prime graphs, and graphs with respect to ideals in near rings. Near ring theory has many applications in areas as diverse as digital computing, sequential mechanics, automata theory, graph theory, and combinatorics. Suitable for researchers and graduate students, this book provides readers with an understanding of near ring theory and its connection to fuzzy ideals and graph theory.

Author: Robert Lockhart
Publisher: Springer Nature
ISBN: 3030817555
Category : Mathematics
Languages : en
Pages : 555

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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.

Author: W. B. Vasantha Kandasamy
Publisher: Infinite Study
ISBN: 1931233667
Category : Mathematics
Languages : en
Pages : 201

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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).

Author: Dinh Van Huynh
Publisher: American Mathematical Soc.
ISBN: 0821887971
Category : Mathematics
Languages : en
Pages : 330

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This volume contains the proceedings of the Ring Theory Session in honor of T. Y. Lam's 70th birthday, at the 31st Ohio State-Denison Mathematics Conference, held from May 25-27, 2012, at The Ohio State University, Columbus, Ohio. Included are expository articles and research papers covering topics such as cyclically presented modules, Eggert's conjecture, the Mittag-Leffler conditions, clean rings, McCoy rings, QF rings, projective and injective modules, Baer modules, and Leavitt path algebras. Graduate students and researchers in many areas of algebra will find this volume valuable as the papers point out many directions for future work; in particular, several articles contain explicit lists of open questions.

Author: Kuncham Syam Prasad
Publisher: World Scientific
ISBN: 981320737X
Category : Mathematics
Languages : en
Pages : 324

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Recent developments in various algebraic structures and the applications of those in different areas play an important role in Science and Technology. One of the best tools to study the non-linear algebraic systems is the theory of Near-rings.The forward note by G

Author: Gilberto Bini
Publisher: Springer Science & Business Media
ISBN: 1461509572
Category : Technology & Engineering
Languages : en
Pages : 181

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Foreword by Dieter Jungnickel Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory. This book will be of interest to both professional and academic researchers in the fields of communication and coding theory. The book is a concrete and self-contained introduction to finite commutative local rings, focusing in particular on Galois and Quasi-Galois rings. The reader is provided with an active and concrete approach to the study of the purely algebraic structure and properties of finite commutative rings (in particular, Galois rings) as well as to their applications to coding theory. Finite Commutative Rings and their Applications is the first to address both theoretical and practical aspects of finite ring theory. The authors provide a practical approach to finite rings through explanatory examples, thereby avoiding an abstract presentation of the subject. The section on Quasi-Galois rings presents new and unpublished results as well. The authors then introduce some applications of finite rings, in particular Galois rings, to coding theory, using a solid algebraic and geometric theoretical background.

Author: Marco Fontana
Publisher: CRC Press
ISBN: 9780203910627
Category : Mathematics
Languages : en
Pages : 524

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Featuring presentations from the Fourth International Conference on Commutative Algebra held in Fez, Morocco, this reference presents trends in the growing area of commutative algebra. With contributions from nearly 50 internationally renowned researchers, the book emphasizes innovative applications and connections to algebraic number theory, geome

Author: Mikhail Chebotar
Publisher: Walter de Gruyter
ISBN: 3110912163
Category : Mathematics
Languages : en
Pages : 177

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Book Description
This volume consists of seven papers related in various matters to the research work of Kostia Beidar†, a distinguished ring theorist and professor of National Ching Kung University (NCKU). Written by leading experts in these areas, the papers also emphasize important applications to other fields of mathematics. Most papers are based on talks that were presented at the memorial conference which was held in March 2005 at NCKU.

Author: A.A. Tuganbaev
Publisher: Springer Science & Business Media
ISBN: 9401598789
Category : Mathematics
Languages : en
Pages : 363

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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.