Compact and Linearly Compact Rings with Identity
by
Jo-Ann Cohen
North Carolina State University

The structure of a compact ring A with identity is often a reflection of the structure of the group G of units in A. For example, if 2 is a unit in A, then A is a commutative (finite) ring if and only if G is an abelian (finite) group.

In this talk, we first describe some of the previous results concerning the structure of compact rings with identity and the strategies used in proving those results. Next, we characterize all compact rings with identity having a simple group of units and generalize those results to obtain a classification of linearly compact rings with identity having a simple group of units and a transfinitely nilpotent Jacobson radical. If time permits, we will continue our discussion of linearly compact rings and describe an analogue of a structure theorem for locally compact rings given by Goldman and Sah (1966).

Date received: May 11, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagw-23.