On (m, n)-semiprime submodules

Abstract

This paper aims to introduce a new class of submodules, called (m, n)-semiprime submodule, which is a generalization of semiprime submodule. Let M be a unital A-module and m, n ∈ N. Then a proper submodule P of M is said to be an (m, n)-semiprime submodule if whenever amx ∈ P for some a ∈ A, x ∈ M, then anx ∈ P. In addition to giving many characterizations and properties of this kind of submodules, we also use them to characterize von Neumann regular modules.

Keywords

• semiprime submodule
• (m
• n)-closed ideal
• (m
• n)-semiprime submodule
• von neumann regular module
• descending chain condition.