ON THE SUBSTRUCTURES ? AND del

Abstract

In this paper, we discuss the question of when the substructures, the singular sub-bimodule Delta[M, N] and the cosingular bi-submodule del[M, N] of Hom(M, N), are equal to zero. Some well-known results of regular rings are obtained. Moreover, the substructures Delta[M, N] and del[M, N] with M and N that are direct sums of submodules are studied.