Rings, modules and radicals [antikvár]

PREFACE Hűs volume contains the papers and the problems presented at the International Colloquium on "Associative Rings, Modules and Radicals" at Keszthely (Lake Balaton), 9-13 August 1971. The colloquium was organized by the Bolyai János Mathematical Society. The Organizing Committee of the colloquium consisted of Professors R. Freud, A- Kertész,]. Pelikán (secretary), L. Rédei (chairman), 0. Steinfeld, F.A. Szász and R. Wiegandt. The concept of ring is one of the oldest and most thoroughly studied algebraic structure, and it is perhaps not only a personal preference to say that the theory of rings is one of the most important fields of algebra. At present, a good many algebraists are interested in ring theoretic problems. Because of the large scope of the theory of rings it seemed to be most desirable to put certain restraints to the topics discussed on the colloquium. Thus the idea that took shape was that the matters of tlie colloquium should be "Associative Rings, Modules and Radicals". Module theory can hardly be separated from ring theory, therefore we wished to include talks on this topic. The theory of non-associative rings, however, had to be excluded, for this would have essentially increased both the number of lectures and of participants. As in the last three decades the interest in the various kinds of radicals and also a general theory of radicals has grown rapidly, it was a particular aim of this colloquium, to lay emphasis upon radical theory and to incite specialists in radical theory to participation. The colloquium was attended by a considerable number of very distinguished algebraists from various countries. Many interesting papers were presented and followed by high level and fruitful discussions. The length of lectures was generally 30 minutes including the time of discussions. There were two parallel sections: "Rings" and "Modules and Radicals". The present volume of the proceedings of the colloquium contains the papers and short communications submitted for publication to the Organizing Committee. A few papers, the authors of which were not able to participate in the colloquium for various reasons, have been added. Professors i.M.^. Maranda, W. Krull and A.G. Kuros had intended to attend the colloquium, but they were, unfortunately, hindered by death. The Organizing Committee decided that the two papers on radical theory of professor - 3