The Theory of Near-Rings
Title | The Theory of Near-Rings PDF eBook |
Author | Robert Lockhart |
Publisher | Springer Nature |
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: The Theory and its Applications
Title | Near-rings: The Theory and its Applications PDF eBook |
Author | |
Publisher | Elsevier |
Pages | 487 |
Release | 2011-10-10 |
Genre | Mathematics |
ISBN | 0080871348 |
Near-rings: The Theory and its Applications
Near-Rings and Near-Fields
Title | Near-Rings and Near-Fields PDF eBook |
Author | G. Betsch |
Publisher | Elsevier |
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.
Smarandache Near-Rings
Title | Smarandache Near-Rings PDF eBook |
Author | W. B. Vasantha Kandasamy |
Publisher | Infinite Study |
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).
Near-rings and Their Links with Groups
Title | Near-rings and Their Links with Groups PDF eBook |
Author | J. D. P. Meldrum |
Publisher | Pitman Advanced Publishing Program |
Pages | 300 |
Release | 1985 |
Genre | Mathematics |
ISBN |
Near-Rings and Near-Fields
Title | Near-Rings and Near-Fields PDF eBook |
Author | Yuen Fong |
Publisher | Springer Science & Business Media |
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.
Rings, Groups, and Algebras
Title | Rings, Groups, and Algebras PDF eBook |
Author | X. Cao |
Publisher | CRC Press |
Pages | 349 |
Release | 2020-12-22 |
Genre | Mathematics |
ISBN | 1000116794 |
"Integrates and summarizes the most significant developments made by Chinese mathematicians in rings, groups, and algebras since the 1950s. Presents both survey articles and recent research results. Examines important topics in Hopf algebra, representation theory, semigroups, finite groups, homology algebra, module theory, valuation theory, and more."