STRONGLY PRIME SUBMODULES

Abstract. Let R be a commutative ring with identity. For an R-module M, the notion of strongly prime submodule of M is defined. It is shown that this notion of prime submodule inherits most of the essential properties of the usual notion of prime ideal. In particular, the Generalized Principal Ideal Theorem is extended to modules. Throughout this paper all rings are commutative with identity and all modules are unitary. Also we consider R to be a ring and M a unitary R-module. For a submodule N of M, let (N: M) denote the set of all elements r in R such that rM ⊆ N. Note that (N: M) is an ideal of R, in fact, (N: M) is th