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.
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