On Primary and Classical Primary Submodules

Abstract

Let R be a commutative ring with identity and M be an R-module. In this paper some properties of primary and classical primary submodules will be investigated. It is shown that if F is a faithfully flat R-module, then Q is a primary submodule of M if and only if F Q is a primary submodule of F M. Also some characterization of classical primary submodules are given. Furthermore, the existence of (minimal) primary submodules containing classical primary submodules are investigated