NEARLY PRIMARY SUBMODULES

Let R be a commutative ring with unity and let N be a submodule of a nonzero left R-module M, N is called primary if whenever rx?N ,r?R,x?M , implies that either x?N or r??([N:M] ). In this paper we say that N is nearly primary, if whenever rx?N ,r?R,x?M, , implies that either x?N+J(M) or r??([N+J(M):M] ) , (in short N.primary),where J(M) is the Jacobson radical of M. We give many results of this type of submodules.