Morita theory for non-unital rings
by
Oleg Smirnov
Department of Mathematics, University of Virginia
Coauthors: J.R. Faulkner

In this talk we discuss a generalization of Morita theory to non-unital rings. We consider the category mod-A of modules M over a ring A which satisfy two conditions:

(A) MA=M,
(B) mA=0 implies m=0.

(C) A_A in mod-A and _AA in A-mod.

Under these assumptions one can develop a complete analog of the classical Morita theory. Particularly, the following is true:

• Categories mod-A and mod-B are equivalent if and only if there exist a Morita context containing A and B.
• Every equivalence from mod-A to mod-B is isomorphic to the functor _  [^(\otimes)]_AU_B. Here [^(\otimes)] is the tensor product in our categories.
• Etc.

We also argue that the conditions (A), (B), and (C) seem to be necessary to develop Morita theory.

Oleg Smirnov's Home Page

Date received: November 15, 1998

Copyright © 1998 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 # cabw-22.