Author : Yuen Fong
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 32,12 MB
Release : 2012-12-06
Category : 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.
Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
Page : 201 pages
File Size : 12,38 MB
Release : 2002
Category : 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).
Author : Robert Lockhart
Publisher : Springer Nature
Page : 555 pages
File Size : 36,64 MB
Release : 2021-11-14
Category : 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.
Author : G. Betsch
Publisher : Elsevier
Page : 313 pages
File Size : 18,17 MB
Release : 2011-09-22
Category : 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.
Author : Kuncham Syam Prasad
Publisher : World Scientific
Page : 324 pages
File Size : 18,58 MB
Release : 2016-11-28
Category : 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
Author :
Publisher : Elsevier
Page : 487 pages
File Size : 15,49 MB
Release : 2011-10-10
Category : Mathematics
ISBN : 0080871348
Near-rings: The Theory and its Applications
Author : Hubert Kiechle
Publisher : Springer Science & Business Media
Page : 338 pages
File Size : 26,13 MB
Release : 2005-04-19
Category : 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.
Author : Craig Huneke
Publisher : Cambridge University Press
Page : 446 pages
File Size : 34,93 MB
Release : 2006-10-12
Category : Mathematics
ISBN : 0521688604
Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Author : Zhe-Xian Wan
Publisher : World Scientific
Page : 360 pages
File Size : 43,92 MB
Release : 2003
Category : 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.
Author : Alexander V. Mikhalev
Publisher : Springer Science & Business Media
Page : 629 pages
File Size : 19,91 MB
Release : 2013-06-29
Category : 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.
