Characterization of ss-supplemented modules with respect to finitely generated factor modules in view of singularity

In this essay (amply) cofinitely ?ss-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 ?ss-perfect ring if and only if every (projective) left R-module is (amply) cofinitely ?ss-supplemented. Moreover, the question when cofinitely ?ss-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 ?ss-supplemented R-module is cofinitely ss-supplemented is proven.