Weakly (m,n)–semiprime submodules

Abstract

This article gives several properties of a new type of submodules, namely weakly ( m, n ) -semiprime submodules where m and n are positive integers satisfying m > n . The primary objectives of the present article are to characterize weakly ( m, n ) - semiprime submodules and to provide a new characterization of the von Neumann regular modules in terms of weakly ( m, n ) -semiprime submodules.