This award provides partial support for Professor Warren May of the University of Arizona to spend four months working with Professor Ruediger Goebel of the Department of Mathematics, University of Essen, West Germany. They will collaborate in the production of a monograph on recent progress in module theory. They will also carry out joint research on problems raised in past collaborations and on new problems. These include questions on the representation of algebras by endomorphisms leaving four subspaces invariant, and questions on endomorphism algebras of modules over complete discrete valuation rings. Mixed modules have received a lot of attention in the past decade, and Essen is a recognized center of excellence in this area of mathematics. Professor May is recognized for his research in the areas of endomorphism rings of mixed groups and group algebras. Professor Goebel is a prolific researcher in the areas of realization of endomorphism rings and automorphism groups. Their collaboration is expected to produce important results that will be applicable in several areas of algebra and other fields.
