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.
SIP modules, SSP modules, extending modules, lifting modules.
ALKAN, MUSTAFA and HARMANCI, ABDULLAH (2002) "On Summand Sum and Summand Intersection Property of Modules," Turkish Journal of Mathematics: Vol. 26: No. 2, Article 1. Available at: https://journals.tubitak.gov.tr/math/vol26/iss2/1