International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 58132, 8 pages
doi:10.1155/2007/58132

δ-Small Submodules and δ-Supplemented Modules

Abstract

Let R be a ring and M a right R-module. It is shown that (1) δ(M) is Noetherian if and only if M satisfies ACC on δ-small submodules; (2) δ(M) is Artinian if and only if M satisfies DCC on δ-small submodules; (3) M is Artinian if and only if M is an amply δ-supplemented module and satisfies DCC on δ-supplement submodules and on δ-small submodules.