Turkish Journal of Mathematics
Abstract
The submodule \overline{Z}(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 (P) if \overline{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 \in Mod-R \overline{Z}_{R}(M) = 0} is closed under factor modules, then R has (P) if and only if the ring R is von Neumann regular.
DOI
10.3906/mat-1210-15
Keywords
von Neumann regular ring, perfect ring, (non)cosingular submodule
First Page
649
Last Page
657
Recommended Citation
TÜTÜNCÜ, D. K, ERTAŞ, N. O, SMITH, P. F, & TRIBAK, R (2014). Some rings for which the cosingular submodule of every module is a direct summand. Turkish Journal of Mathematics 38 (4): 649-657. https://doi.org/10.3906/mat-1210-15
