ON WEAKLY PRIME AND ALMOST PRIME SUBMODULES

Let R be a commutative ring with identity and M be a unitary R-module. Suppose n;m ¸ 2 are positive integers. In this paper, we define (n¡1; n)¡weakly prime and (n¡1; n)¡m-almost prime submodules. Modules with the property that, every proper submodule is (n ¡ 1; n)¡weakly prime ((n¡1; n)¡n¡almost prime), are characterized and we show that under some assumptions (n¡1; n)-prime submodules and (n¡1; n)¡m-almost prime submodules coincide (n;m ¸ 2).