Primeness in Module Category

Abstract

We introduce the notion of prime submodules of a given right R-module and describe all properties of them as a generalization of prime ideals in associative rings.

Max CS and min CS modules

“…We denote the uniform dimension of the module M R by u-dim(M R ). For a submodule X of M, we write We adopt the notions of primeness and semiprimeness in module category introduced by Sanh et al in [7]. Recall that a min CS module ( [2] and [8].…”