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.

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.

It is by no means clear what comprises the "heart" or "core" of algebra, the part of algebra which every algebraist should know. Hence we feel that a book on "our heart" might be useful. We have tried to catch this heart in a collection of about 150 short sections, written by leading algebraists in these areas. These sections are organized in 9 chapters A, B, . . . , I. Of course, the selection is partly based on personal preferences, and we ask you for your understanding if some selections do not meet your taste (for unknown reasons, we only had problems in the chapter "Groups" to get enough articles in time). We hope that this book sets up a standard of what all algebraists are supposed to know in "their" chapters; interested people from other areas should be able to get a quick idea about the area. So the target group consists of anyone interested in algebra, from graduate students to established researchers, including those who want to obtain a quick overview or a better understanding of our selected topics. The prerequisites are something like the contents of standard textbooks on higher algebra. This book should also enable the reader to read the "big" Handbook (Hazewinkel 1999-) and other handbooks. In case of multiple authors, the authors are listed alphabetically; so their order has nothing to do with the amounts of their contributions.

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.

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.