ON Socale-Prime Submodules

Abstract

Let R be a commutative with non-zero identity, let A be a R-module. In this paper submodule H of an R-module A to be Soc-prime if whenever r ∈ R, a ∈ A with < a > ≤ Soc(A) and ra ∈ H then either a ∈ H or r ∈ [H: A]. We give a number of characterizations of Soc-prime submodules.