On Summand Sum and Summand Intersection Property of Modules

Authors : Mustafa ALKAN, Abdullah HARMANCI

Pages : 131-148

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :R will be an associative ring with identity and modules M will be unital left R- modules. In this work, extending modules and lifting modules with the SSP insert ignore into journalissuearticles values(or SIP); are studied. A necessary and sufficient condition for a module M to have the SSP is that for every decomposition M = A\oplus B and f\in Hominsert ignore into journalissuearticles values(A,B);, Iminsert ignore into journalissuearticles values(f); is a direct summand of B. Among others it is shown also that a insert ignore into journalissuearticles values(C3); module with the SIP has the SSP, and a insert ignore into journalissuearticles values(D3); module with SSP has the SIP.
Keywords : SIP modules, SSP modules, extending modules, lifting modules