Coprimely Structured Modules

Abstract

Let R be a commutative ring with identity. A prime submodule P of an R-module M is called coprimely structured if, whenever P is coprime to each element of an arbitrary family of submodules of M, the intersection of the family is not contained in P. An R-module M is called coprimely structured provided each prime submodule of M is coprimely structured. In this paper, properties of coprimely structured modules are examined. Severals results for coprimely structured finitely generated modules and coprimely structured multiplication modules are obtained.