On CS-modules over Goldie rings.
type: Item
instance of: scholarly article
title: On CS-modules over Goldie rings.
zbMATH Open document ID: 1057.16005
author: Mahmoud Ahmed Kamal
published in: Journal of the Egyptian Mathematical Society
publication date: 2004-06-18T00:00:00Z
review text: CS-modules, i.e. modules in which every closed submodule is a direct summand, and their structure have been studied extensively since the middle 1980s. This paper takes the study further by investigating the structure of nonsingular CS-modules over a ring with finite right uniform dimension and of CS-modules over semiprime or prime right Goldie rings. For rings with finite uniform dimension, it is proven that a module over a nonsingular ring is a CS-module if and only if it is a 1-CS-module and every local summand is a summand. It is shown that the study of nonsingular modules over a semiprime right Goldie ring can be reduced to the study of modules which contain no nontrivial injective submodules. Characterizations of all nonsingular CS-modules over a semiprime right Goldie ring as well as of CS-modules over a prime right Goldie ring are found.
reviewed by: Frieda Theron
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16D80
Mathematics Subject Classification ID: 16P60
Mathematics Subject Classification ID: 16E10
zbMATH DE Number: 2076133
zbMATH Keywords: CS-modules
zbMATH Keywords: closed submodules
zbMATH Keywords: nonsingular modules
zbMATH Keywords: right uniform dimension
zbMATH Keywords: semiprime right Goldie rings
zbMATH Keywords: prime right Goldie rings
zbMATH Keywords: uniform modules
zbMATH Keywords: Noetherian rings
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2076133