Author/Authors :
TÜTÜNCÜ, DERYA KESKİN Hacettepe University - Department of Mathematics, Turkey , ERTAŞ, NİL ORHAN Karabuk University - Department of Mathematics, Turkey , SMITH, PATRICK F Glasgow University - Department of Mathematics, Scotland , TRIBAK, RACHID Regional Center for Career Education and Training (CRMEF), Morocco
Abstract :
The submodule Z(M) = ∩{N | M/N is small in its injective hull} was introduced by Talebi and Vanaja in 2002. A ring R is said to have property (P) if Z(M) is a direct summand of M for every R-module M . It is shown that a commutative perfect ring R has (P) if and only if R is semisimple. An example is given to show that this characterization is not true for noncommutative rings. We prove that if R is a commutative ring such that the class {M ∈ M od − R | ZR(M) = 0} is closed under factor modules, then R has (P) if and only if the ring R is von Neumann regular.
