On d-Small Prime Modules

Abstract

Abstract Let R be a commutative ring with an identity, and D be an unitary fi-module. We say a non-zero submodule E of D is d-small prime if for each c ∈ R, d ∈ D, (d) «d D with cd ∈ E, then either d ∈ E or c ∈ [E: D] and an fi-module D is a d-small prime if annD = annE for each non-zero submodule E d-small in D. We have given and demonstrated some of the characterizations and features of these types of submodules (modules) in this paper.