CSSES-MODULES and CSSES-RINGS

Abdurzak LEGHWEL, Abdullah HARMANCI
1.704 414

Abstract


ABSTRACT

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.


Keywords


Key Words: CSSES-module and ring, QF-ring, Kasch ring, CEP-ring, semiperfect module and ring, CF-ring

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