Full Description
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.
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.
