CSSES-MODULES and CSSES-RINGS

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

Abstract

Bu çalışmada has desteğee sahip yarıtam CS-modüllerin yapısını araştıracağız. Eğer M modülü has desteğe sahip yarıtam CS-modülse M modülüne CSSES-modül denir. Sağ R-modül RR CSSES-modül ise R halkasına sağ CSSES-halkası denir. Bu çalışmada, diğer ispatladıklarımız yanında, aşağıdakilari de ispalayacağız: [i] Eğer R halkası sağ CF ise ve sol GIN-halka ise, o zaman R bir QF-halkadır ancak ve ancak R bir sağ CS-halkadır ancak ve ancak R bir sağ CSSES- halkadır. [ii] Her sol Kasch ve sağ CF-halka sağ CSSES-halkadır. [iii] Eğer R sağ ve sol destekleri eşit sol Kasch sağ IN-halka ise , o zaman R CSSES-halkadır

Keywords

• CSSES-modül ve halka, QF-halka, Kasch halka, CEP-halka, yarıtam modül ve halka, CF-halka

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