Krull-Schmidt Theorem: Recent Developments
by
Alberto Facchini
Universita di Padova

Some recent developments of the Krull-Schmidt Theorem will be presented. After a brief historical presentation, I will talk about the Krull-Schmidt Theorem for various algebraic structures. Then I will move on to consider the case of modules over associative rings. The case of serial modules will be presented. (Recall that a module is uniserial if its lattice of submodules is linearly ordered by inclusion, and is serial if it is a direct sum of uniserial modules.) In this context the notions of monogeny classes and epigeny classes appear naturally. I will present some recent results by Puninski, Diracca and myself about the uniqueness of decompositions and the uniqueness of the monogeny/epigeny classes. Finally, I will consider the extension from local endomorphism rings to homogeneous semilocal endomorphism rings, that is, rings that are simple artinian modulo their Jacobson radical.

Date received: February 23, 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 # cage-08.