CHARACTERIZATION OF ss-SUPPLEMENTED MODULES WITH RESPECT TO FINITELY GENERATED FACTOR MODULES IN VIEW OF SINGULARITY

Abstract

Abstract

In this essay (amply) cofinitely δss-supplemented modules are presented and fundamental algebraic features of these modules are examined. Privately, a ring characterization theorem is presented as follows. R is a δss-perfect ring if and only if every (projective) left Rmodule is (amply) cofinitely δss-supplemented. Moreover, the question when cofinitely δss-supplemented modules are cofinitely ss-supplemented is checked. With this aim we define left ∆ss-rings and the fact that a ring R is a left ∆ss-ring if and only if each cofinitely δss-supplemented R-module is cofinitely ss-supplemented is proven.