R-Annihilator - Hollow Modules

Hala K. Al-Hurmuzy
Abstract: Let R be an associative ring with identity and let M be a unitary left R- module .We call a non-zero module M, R-annihilator ?hollow module if every proper submodule of M is R-annihilator?small submodule of M..The sum ? A?_M of all such submodules of M contains the Jacobson radical J(M) and the singular submodule Z(M).When M is finitly generated and faithful, we study? A?_M and ? K?_M in this paper .Conditions when? A?_M is R-annihilator-small and? K?_M=? A?_(M ), J(M) ?? A?_Mand Z(M)?? A?_M are given .
Keywords: hollow modules, annihilators, R-annihilator- hollow modules., Research Paper, Mathematics, Iraq
PDF Link: https://www.ijsr.net/archive/v7i1/ART20178614.pdf