Abstract :
Let R be a commutative ring with identity and let M be a unitary left R module. We call the R-module M kerquasi-injective if for every monomorphism f from N into Q(M) , where N is a submodule of Q(M) and Q(M) is a quasi-injective hull of (M) and for every homomorphism g from N into M there exists a homomorphism h from Q(M) into M such that ker hf subset of ker g It is clear that every quasi-injective module is kerquasi-injective, however the converse is false. Also every ker-injective module is kerquasi-injective, however the converse is false. In this paper we give some characterizations of kerquasi-injective modules, we also study some conditions under which a kerqausi-injective module becomes quasi-injective. For example, if a kerquasi-injective module is a finitely generated, then it is a quasi-injective. We ought to mention that we were not able to give an example of a kerquasi-injective module which is not quasi-injective and ker-injective.
