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

Küçük Resim Yok

Tarih

2014

Dergi Başlığı

Dergi ISSN

Cilt Başlığı

Yayıncı

Tubitak Scientific & Technological Research Council Turkey

Erişim Hakkı

info:eu-repo/semantics/openAccess

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.

Açıklama

Anahtar Kelimeler

von Neumann regular ring, perfect ring, (non)cosingular submodule

Kaynak

Turkish Journal of Mathematics

WoS Q Değeri

Q4

Scopus Q Değeri

Q2

Cilt

38

Sayı

4

Künye