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 is an element of N. Then a proper submodule P of M is said to be an (m, n)-semiprime submodule if whenever a(m)x is an element of P for some a is an element of A,x is an element of M, then a(n)x is an element of P. In addition to giving many characterizations and properties of this kind of submodules, we also use them to characterize von Neumann regular modules.