The Theory of Near-Rings

by Robert Lockhart

Overview

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.

Product Details

ISBN-13:	9783030817558
Publisher:	Springer International Publishing
Publication date:	11/14/2021
Series:	Lecture Notes in Mathematics , #2295
Sold by:	Barnes & Noble
Format:	eBook
File size:	18 MB
Note:	This product may take a few minutes to download.

About the Author

Robert Lockhart has worked in mathematics at universities in London, Nigeria, New Guinea, Brunei, Milton Keynes and Oxford, where he also worked simultaneously in computing. He has enjoyed a parallel career in computing, as one of the original programmer-designers for the multi award-winning British Telecom Prestel project, as part of a research project funded by the European Union, and at the Atlas laboratory for the Rutherford–Appleton laboratory. He has published research papers on algebra, conservation biology, and modern computing. For the past twenty years he has worked mainly in distance and online education. Throughout his career he has been a regular contributor to near-ring conferences and a member of the London Mathematical Society.

Table of Contents

1 Stems, Mappings and Near-Rings.- 2 Near-Ring Theory.- 3 Near-Fields.- 4 Near-Rings on Groups with Low Order.- 5 Near-Rings on Some Families of Groups.- 6 Near-Rings Hosted by p-Groups and Related Groups.- 7 Transformation Near-Rings.- 8 Generalisations and Sub-Near-Rings of Transformation Near-Rings.- 9 Phomomorphisms.- 10 Specific Examples.- 11 Modules.- 12 Radicals.- 13 Matrices.- 14 F-Near-Rings.- 15 Product Theory.- 16 Product Theory on Finite Elementary Abelian Groups.- A Isotopy.- B Near-Ring Products on D₄.- C Other Structures of Interest.- D Semi-Linear Mappings.- E Zsigmondy's Theorem.- Bibliography.- Afterword.- Index.

Editorial Reviews

This book is a substantial account … of almost all known aspects of near-ring theory. … It should therefore be regarded as a rich source of known results on various aspects of near-ring theory … . This makes the book an important asset to the near-ring researcher's library. … This book is a massive undertaking by the author, and he should be commended for it. … it is highly recommended to order the book for your library as an excellent work of reference.” (Johan H. Meyer, Mathematical Reviews, January, 2023)

“The book is interesting, and could be useful to researchers and students.” (Bijan Davvaz, zbMATH 1498.16001, 2022)

From the Publisher