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


KESKİN TÜTÜNCÜ D., ORHAN ERTAŞ N. , Smith P. F. , Tribak R.

TURKISH JOURNAL OF MATHEMATICS, cilt.38, ss.649-657, 2014 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 38 Konu: 4
  • Basım Tarihi: 2014
  • Doi Numarası: 10.3906/mat-1210-15
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Sayfa Sayıları: ss.649-657

Özet

The snbmodule (Z)overbar(M) = boolean AND{N vertical bar 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)overbar(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 is an element of Mod-R vertical bar <(Z)overbar >(R)(M) = 0} is closed under factor modules, then R has (P) if and only if the ring R is von Neumann regular.