ON WEAKLY PRIME SUBMODULES

Let R be a commutative ring with non-zero identity. We define a proper submodule N of an R-module M to be weakly prime if 0 not equal rm is an element of N(r is an element of E R, m is an element of E M) implies m is an element of N or r M subset of N. A number of results concerning weakly prime submodules are given. For example, we give three other characterizations of weakly prime submodules.