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

In this essay (amply) cofinitely delta(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 delta(ss)-perfect ring if and only if every (projective) left R-module is (amply) cofinitely delta(ss)-supplemented. Moreover, the question when cofinitely delta(ss)-supplemented modules are cofinitely sssupplemented is checked. With this aim we define left triangle(ss)-rings and the fact that a ring R is a left triangle(ss)-ring if and only if each cofinitely delta(ss)-supplemented R-module is cofinitely ss-supplemented is proven.