Preinjective modules and finite representation type of Artinian rings
by
Nguyen Viet Dung
Department of Mathematics, Ohio University

A finitely presented indecomposable right module M over a Krull-Schmidt ring R is called preinjective if there is a finitely presented right R-module K such that M is not isomorphic to a direct summand of K and for any finitely presented right R-module N such that N and K contain no isomorphic indecomposable direct summands, any monomorphism from M to N splits. We show that if R is an Artinian ring which either has a Morita self-duality or is a PI-ring, then R is of finite representation type if and only if every finitely presented right R-module is of finite endolength and R has only finitely many non-isomorphic preinjective right R-modules. This provides a generalization of Herzog's result on the validity of the pure semisimple conjecture for rings with Morita self-duality and for PI-rings.

Date received: March 22, 1999

Copyright © 1999 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 # cabz-08.