نجمه دهقانی

The notion of extending modules has been generalized to purely extending, by John Clark. We generalize the notions of C2 and C3, via two ways, by using purity. We say that a module MR has P.C2 (G.P.C2) property if every submodule isomorphic to a pure submodule (direct summand) of MR is a pure submodule. Moreover, we say that a module MR has P.C3 (G.P.C3) property whenever the sum of two independent pure submodules (direct summands) of MR is a pure submodule. We study general properties of these modules and investigate the relations between them.