Proceedings of the Third International Algebra Conference

This volume contains one invited lecture which was presented by the 1994 Fields Medal­ ist Professor E. Zelmanov and twelve other papers which were presented at the Third International Conference on Algebra and Their Related Topics at Chang Jung Christian University, Tainan, Republic of China, during the period June 26-July 1, 200l. All papers in this volume have been refereed by an international referee board and we would like to express our deepest thanks to all the referees who were so helpful and punctual in submitting their reports. Thanks are also due to the Promotion and Research Center of National Science Council of Republic of China and the Chang Jung Christian University for their generous financial support of this conference. The spirit of this conference is a continuation of the last two International Tainan­ Moscow Algebra Workshop on Algebras and Their Related Topics which were held in the mid-90's of the last century. The purpose of this very conference was to give a clear picture of the recent development and research in the fields of different kinds of algebras both in Taiwan and in the rest ofthe world, especially say, Russia" Europe, North America and South America. Thus, we were hoping to enhance the possibility of future cooperation in research work among the algebraists ofthe five continents. Here we would like to point out that this algebra gathering will constantly be held in the future in the southern part of Taiwan.

Inhalt

Preface. A survey on polynomials and polynomial and compatible structures; E. Aichinger, G.F. Pilz. Gröbner-Shirshov bases for algebras, groups and semigroups; L. Bokut, Y. Fong, L.-S. Shiao. Sylow-2 subgroups of finite simple groups; K. Harada, Mong Lung Lang. Combinatorial representation theory and crystal bases; Seok-Jin Kang. On some problems in PI-theory in characteristic p connects with dividing by p; A. Kemer. Quantum Lie algebras and related problems; V.K. Kharchenko. Gröbner-Shirshov bases for representations of Lie algebras and Hecke algebras of type A; Kyu-Hwan Lee. The existence of a simple nil ring (after Agata Smoktunowicz); I.V. L'vov. Locally nilpotent derivations on the surface xy = p(z); L. Makar-Limanov. Division algebras; L.H. Rowen. R[x,y] is Brown-McCoy radical if R is Jacobson radical; A. Smoktunowicz. Applications of dualizing complexes; Q.-S. Wu, J.J. Zhang. Idempotents in conformal algebras; E. Zelmanov.