ON it-ESSENTIAL AND u-M-SINGULAR MODULES

摘要

As a generalization of essential submodules Zhou defines a a-essential submod-ule provided it has a non-zero intersection with any non-zero submodule in forany class μ. Let M be a module. In this article we study δ—essential submodulesas a dual of 5-small submodules of Zhou where δ= {NE o-[M] :Rej(N, M) =-0} and M = {N E : N N}, and also define μ-M—singular modulesas modules N E a[M] such that N K / L for some K E τ[M] and L isu—essential in K. By M—M—singular modules and δ—M—singular modules acharacterization of GCO—modules, and by FC—M—singular modules where .PCis the class of finitely cogenerated modules, a characterization of semisimpleArtinian rings are given.