On second socles of finitely cogenerated injective modules

Abstract

finitely cogenerated seminoetherian right R-module is of finite length (Theorem 5). Here, seminoetherian modules mean modules whose every nonzero submodule contains a maximal submodule. As a corollary, we obtain the theorem of Clark and Huynh (Corollary 7). Also we point out a condition for certain right perfect rings to have Morita duality (Corollary 10). In the last part of this note, we mention a dual of Theorem 5 (Theorem 13).