Near-Rings and Near-Fields

Near-Rings and Near-Fields
Author: Yuen Fong
Publisher: Springer Science & Business Media
Total Pages: 271
Release: 2012-12-06
Genre: Mathematics
ISBN: 9401103593

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.

Smarandache Near-Rings

Smarandache Near-Rings
Author: W. B. Vasantha Kandasamy
Publisher: Infinite Study
Total Pages: 201
Release: 2002
Genre: Mathematics
ISBN: 1931233667

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).

The Theory of Near-Rings

The Theory of Near-Rings
Author: Robert Lockhart
Publisher: Springer Nature
Total Pages: 555
Release: 2021-11-14
Genre: Mathematics
ISBN: 3030817555

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.

Near-Rings and Near-Fields

Near-Rings and Near-Fields
Author: G. Betsch
Publisher: Elsevier
Total Pages: 313
Release: 2011-09-22
Genre: Mathematics
ISBN: 0080872484

Most topics in near-ring and near-field theory are treated here, along with an extensive introduction to the theory.There are two invited lectures: ``Non-Commutative Geometry, Near-Rings and Near-Fields'' which indicates the relevance of near-rings and near-fields for geometry, while ``Pseudo-Finite Near-Fields'' shows the impressive power of model theoretic methods. The remaining papers cover such topics as D.G. near-rings, radical theory, KT-near-fields, matrix near-rings, and applications to systems theory.

Nearrings, Nearfields And Related Topics

Nearrings, Nearfields And Related Topics
Author: Kuncham Syam Prasad
Publisher: World Scientific
Total Pages: 324
Release: 2016-11-28
Genre: Mathematics
ISBN: 981320737X

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

Nearrings and Nearfields

Nearrings and Nearfields
Author: Hubert Kiechle
Publisher: Springer Science & Business Media
Total Pages: 338
Release: 2005-04-19
Genre: Mathematics
ISBN: 9781402033902

The present volume is the Proceedings of the 18th International Conference on Nearrings and Nearfields held at the Helmut-Schmidt-Universität, Universität der Bundeswehr Hamburg, from July 27 – August 3, 2003. It contains the written versions of the lectures by the five invited speakers. These concern recent developments of planar nearrings, nearrings of mappings, group nearrings and loop-nearrings. One of them is a long and very substantial research paper "The Z-Constrained Conjecture". They are followed by 13 contributions reflecting the diversity of the subject of nearrings and related structures. Besides the purely algebraic structure theory these papers show many connections of nearring theory with group theory, combinatorics, geometries, and topology. They all contain original research.

The Concise Handbook of Algebra

The Concise Handbook of Algebra
Author: Alexander V. Mikhalev
Publisher: Springer Science & Business Media
Total Pages: 629
Release: 2013-06-29
Genre: Mathematics
ISBN: 9401732671

It is by no means clear what comprises the "heart" or "core" of algebra, the part of algebra which every algebraist should know. Hence we feel that a book on "our heart" might be useful. We have tried to catch this heart in a collection of about 150 short sections, written by leading algebraists in these areas. These sections are organized in 9 chapters A, B, . . . , I. Of course, the selection is partly based on personal preferences, and we ask you for your understanding if some selections do not meet your taste (for unknown reasons, we only had problems in the chapter "Groups" to get enough articles in time). We hope that this book sets up a standard of what all algebraists are supposed to know in "their" chapters; interested people from other areas should be able to get a quick idea about the area. So the target group consists of anyone interested in algebra, from graduate students to established researchers, including those who want to obtain a quick overview or a better understanding of our selected topics. The prerequisites are something like the contents of standard textbooks on higher algebra. This book should also enable the reader to read the "big" Handbook (Hazewinkel 1999-) and other handbooks. In case of multiple authors, the authors are listed alphabetically; so their order has nothing to do with the amounts of their contributions.

Nearrings, Nearfields and K-Loops

Nearrings, Nearfields and K-Loops
Author: Gerhard Saad
Publisher: Springer Science & Business Media
Total Pages: 449
Release: 2012-12-06
Genre: Mathematics
ISBN: 9400914814

This present volume is the Proceedings of the 14th International Conference on Near rings and Nearfields held in Hamburg at the Universitiit der Bundeswehr Hamburg, from July 30 to August 06, 1995. This Conference was attended by 70 mathematicians and many accompanying persons who represented 22 different countries from all five continents. Thus it was the largest conference devoted entirely to nearrings and nearfields. The first of these conferences took place in 1968 at the Mathematische For schungsinstitut Oberwolfach, Germany. This was also the site of the conferences in 1972, 1976, 1980 and 1989. The other eight conferences held before the Hamburg Conference took place in eight different countries. For details about this and, more over, for a general historical overview of the development of the subject, we refer to the article "On the beginnings and development of near-ring theory" by G. Betsch [3]. During the last forty years the theory of nearrings and related algebraic struc tures like nearfields, nearmodules, nearalgebras and seminearrings has developed into an extensive branch of algebra with its own features. In its position between group theory and ring theory, this relatively young branch of algebra has not only a close relationship to these two more well-known areas of algebra, but it also has, just as these two theories, very intensive connections to many further branches of mathematics.

Lectures on Finite Fields and Galois Rings

Lectures on Finite Fields and Galois Rings
Author: Zhe-Xian Wan
Publisher: World Scientific
Total Pages: 360
Release: 2003
Genre: Mathematics
ISBN: 9789812385703

This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fields are emphasised. In particular, the construction of irreducible polynomials and the normal basis of finite fields are included. The essentials of Galois rings are also presented. This invaluable book has been written in a friendly style, so that lecturers can easily use it as a text and students can use it for self-study. A great number of exercises have been incorporated.