CSSES-MODULES and CSSES-RINGS
We study the structure of semiperfect, CS-Modules with essential socle. We call the module M CSSES-module if M is semiperfect, CS-module with essential socle. We will call the ring R right CSSES-ring if the right R-module RR is CSSESmodule. In this note among others we prove that [i] If R is right CF and left GINring, then R is QF-ring if and only if R is right CS-ring if and only R is CSSESring. [ii] Every left Kasch right CF-ring is right CSSES-ring. [iii] If R is left Kasch and right IN-ring with equal left and right socles, then R is CSSES-ring.