Some rings for which the cosingular submodule of every module is a direct summand

Authors : Derya Keskin TÜTÜNCÜ, Nil Orhan ERTAŞ, Patrick F. SMITH, Rachid TRIBAK

Pages : 649-657

Doi:10.3906/mat-1210-15

View : 9 | Download : 3

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :The submodule \overline{Z}insert ignore into journalissuearticles values(M); = \cap {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 insert ignore into journalissuearticles values(P); if \overline{Z}insert ignore into journalissuearticles values(M); is a direct summand of M for every R-module M. It is shown that a commutative perfect ring R has insert ignore into journalissuearticles values(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 \in Mod-R | \overline{Z}Rinsert ignore into journalissuearticles values(M); = 0} is closed under factor modules, then R has insert ignore into journalissuearticles values(P); if and only if the ring R is von Neumann regular.
Keywords : von Neumann regular ring, perfect ring, non, cosingular submodule