Near-Rings and Near-Fields : Proceedings of the Conference on Near-Rings and Near-Fields, Stellenbosch, South Africa, July 9–16, 1997

The present volume contains the written version of three invited lectures and sixteen papers presented in the International Conference on Near-Rings and Near-Fields held in Stellenbosch, South Africa. These articles reflect contemporary research activities on the algebraic structure theory of near-rings and the interaction they have with group theory, geometry and combinatorics. Audience: This book will be of value to graduate students of mathematics and algebraists interested in all aspects of the near-ring theory. Front Matter....Pages i-vii Combinatorial Aspects of Nearring Theory to the Memory of James Ray Clay....Pages 1-9 Left Self-Distributive Rings and Nearrings....Pages 10-22 On the Development of Matrix Nearrings and Related Nearrings Over the Past Decade....Pages 23-34 The use of Computers in Near-Ring Theory....Pages 35-41 Some Results on Derivations in Nearrings....Pages 42-46 Weakly Divisible Nearrings: Genesis, Construction and their Links with Designs....Pages 47-71 On Semi-Endomorphisms of Abelian Groups....Pages 72-78 A Note on Pseudo-Distributivity in Group Near-Rings....Pages 79-83 The Almost Nilpotent Radical for Near Rings....Pages 84-93 Polynomial Near-Rings in Several Variables....Pages 94-102 s -Primitive ideals in Matrix Near-Rings....Pages 103-107 Essential ideals and R -Subgroups in Near-Rings....Pages 108-117 Conditions that M A ( G ) is a ring....Pages 118-121 On Dependence and Independence in Near-Rings....Pages 122-129 On Modules of Homogeneous Mappings....Pages 130-132 The Number of Isomorphism Classes of D. G. Near-Rings on the Generalized Quaternion Groups....Pages 133-137 When is a centralizer near-ring isomorphic to a matrix near-ring? Part 2....Pages 138-150 Topology and Primary N -Groups....Pages 151-197 On the Radicals of Composition Near-Rings....Pages 198-201 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. The present volume contains the written version of three invited lectures and sixteen papers presented in the International Conference on Near-Rings and Near-Fields held in Stellenbosch, South Africa. These articles reflect contemporary research activities on the algebraic structure theory of near-rings and the interaction they have with group theory, geometry and combinatorics. __Audience:__ Proceedings of the Conference on Near-Rings and Near-Fields, Stellenbosch, South Africa, July 9-16, 1997