Essential Submodules with respect to an Arbitrary Submodule

Abstract

The concept of essential submodules is a well known concept.In this paper we try to replace an arbitrary submodule of M,say T, instead of 0 in the definition of essential submodules. By this,essential submodules are precisely {0}-essential submodules. For a submoduleK of right R-module M, we have K ess M if and only if(K : m) is annr(m)-essential right ideal of R, for each m 2 M \ {0}.Among other things, this generalization of essential submodules gives anecessary and sufficient condition for MT being finitely co-generated.