Abstract: Many applications of algebra require a deep understanding of non-commutative rings and of the structure of modules over such rings. Unfortunately, the rich structure theory available for modules over integral domains appears to be not available in this more general setting. This lecture demonstrates that this is not the case by presenting an approach to studying modules over rings without requiring immediate restrictions on the ring. As most results in module-theory, our discussion has its roots in the theory of linear transformations of a (finite-dimensional) vector-space V. For a given right module M over a ring R, we consider the group E = E(M) of all R-linear transformations M ® M. Composition of maps makes E a ring, and M an E-R-bimodule. The ring E is called the endomorphism ring of M. We will discuss how ring-theoretic properties of the ring E are reflected in the structure of the module M and vice-versa. Examples of applications of this approach to several problems in Algebra will be given.

Brief Biography of the Speaker:
Education:
Universitat Essen Vordiplom (B.S.) 1978
Universitat Essen Diplom (M.S.) 1980
New Mexico State University Ph.D. 1982
Universitat Duisburg Habilitation 1986
Positions Held:
New Mexico State University Graduate Assistant 8/1980 - 5/1982
Universitat Essen Wissenschafliche Hilfskraft 5/1982 - 8/1982
Universitat Duisburg Wissenschaftlicher Angestellter 9/1982 - 8/1983
Marshall University Assistant Professor 8/1983 - 5/1984
Auburn University Assistant Professor 6/1984 - 9/1987
Auburn University Associate Professor 9/1987 - 9/1994
Auburn University Professor 9/1994 - 3/2000
Auburn University Professor and Chair 3/2000 - present
Areas of Research:
Abelian Groups, Ring Theory, Module Theory, Homological Algebra
Talks and Colloquia:
57 talks and colloquia
Papers in Refereed Journals:
60 appeared, 5 accepted, 5 submitted