Synopses & Reviews
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.
Synopsis
This volume contains three invited lectures and sixteen other papers which were pre- sented at the 14th International Conference on Nearrings and Nearfields held in Stellen- bosch, South Africa, July 9-161997. It was also the first nearring conference to be held after the untimely death of James R Clay, who over the years had been an inspiration to many algebraists interested in nearring theory. The occasion was marked by the invitedtalk of Gerhard Betsch, which was devoted to an overview of Clay's contributions to nearring and nearfield theory. This book is affectionately dedicated to the memory of James R Clay. All the papers presented here have been refereed under the supervision of the Editorial Board: Fong Yuen, Carl Maxson, John Meldrum, GUnterPilz, Leon van Wyk and Andries van der Walt. Thanks are due to the referees and to the Editorial Board. A special word of thanks is due to Wen-fong Ke for preparing the final version of the TEX files, and to Fong Yuen for his pains in arranging for the publication of the volume with Kluwer Academic Publishers. Andries van der Walt Stellenbosch, August 1999 COMBINATORIAL ASPECTS OF NEARRING THEORY TO THE MEMORY OF JAMES RAY CLAY GERHARDBETSCH A briefcurriculum vitae ofJames Ray (Jim) Clay Born November5,1938 at Burley (Idaho). Died January 16, 1996 at Tucson (Arizona). Married since 1959 to Carol Cline BURGE, "a truly beautiful daughter of Zion" (Dedication ofJim's 1992 book). Three daughters, ten grand-children.
Table of Contents
Foreword. Invited talks. Combinatorial aspects of nearring theory; To the memory of James Ray Clay; G. Betsch. Left self-distributive rings and nearrings; G.F. Birkenmeier. On the development of matrix nearrings and related nearrings over the past decade; I.J.H. Meyer. Contributed papers. The use of computers in near-ring theory; E. Aichinger, et al. Some results on derivations in nearrings; N. Argaç, H.E. Bell. Weakly divisible nearrings: genesis, construction and their links with designs; A. Benini, et al. On semi-endomorphisms of Abelian groups; Yuen Fong, et al. A note on pseudo-distributivity in group near-rings; R.L. Fray. The almost nilpotent radical for near rings; N.J. Groenewald. Polynomial near-rings in several variables; J. Gutierrez, C. Ruiz de Velasco. s-primitive ideals in matrix near-rings; J.F.T. Hartney, S. Mavhungu. Essential ideals and R-subgroups in near-rings; A.A.M. Kamal. Conditions that MA(G) is a ring; Fu-an Li. On dependence and independence in near-rings; H. McGilvray, C.J. Maxson. On modules of homogeneous mappings; D. Niewieczerzal. The number of isomorphism classes of d.g. near-rings on the generalized quaternion groups; C. Nöbauer. Matrix near-ring? Part 2; A. Oswald, et al. Topology and primary N-groups; S.D. Scott. On the radicals of composition near-rings; S. Veldsman.