We say an R-module M has the generalized summand intersection property (briefly $GSIP$), if the intersection of any two direct summands is isomorphic to a direct summand. This is a generalization of SIP modules. In this note, the characterization of this property over rings and modules is investigated and some useful propositions obtained in SIP modules are generalized to GSIP modules.
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Taşdemır et al. (2018) studied this question.
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