On Summand Sum and Summand Intersection Property of Modules

Authors: MUSTAFA ALKAN, ABDULLAH HARMANCI

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 (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 Hom(A,B), Im(f) is a direct summand of B. Among others it is shown also that a (C_3) module with the SIP has the SSP, and a (D_3) module with SSP has the SIP.

Keywords: SIP modules, SSP modules, extending modules, lifting modules.

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