Characterizations of right perfect rings by \oplus-supplemented modules
by
Derya Keskin
Department of Mathematics Hacettepe University 06532 Beytepe Ankara TURKEY

The aim of this note is to characterize right perfect rings by \oplus-supplemented modules. Let R be a ring. We prove that R is a right perfect ring if and only if every \pi-projective R-module is supplemented (quasi-discrete, lifting, amply supplemented, H-supplemented, \oplus-supplemented and completely \oplus-supplemented, respectively). In this note we also try to investigate supplements of any direct summand of a module M. Let R be a right perfect ring and M=M₁\oplusM₂ a direct sum of submodules M₁ and M₂. We prove that K is a supplement of M₁ in M if and only if K={ f(p)-j(p) | p in P } for some j in Hom(P, M₁), where f : P --> M₂ is a projective cover of M₂.

Date received: November 5, 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-09.