\(\aleph _ 0\)-continuous modules
type: Item
instance of: scholarly article
title: \(\aleph _ 0\)-continuous modules
zbMATH Open document ID: 0579.16007
author: Mamoru Kutami
published in: Osaka Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: A module M is called \(\aleph_ 0\)-continuous if every countably- generated submodule K is essential in some direct summand N of M, and any submodule of M isomorphic to N is also a direct summand of M. The author studies non-singular \(\aleph_ 0\)-continuous modules over regular (in the sense of von Neumann) rings, extending a result of Goodearl. He shows that, for a non-singular \(\aleph_ 0\)-continuous module M over a regular ring, M has no proper direct summand isomorphic to M if and only if \(E_{{\mathcal F}}(M)\) has the same property, where \(E_{{\mathcal F}}(M)\) is the submodule of M consisting of all elements in the injective hull of M which are sent into M by some countably generated essential right ideal of R.
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16D80
zbMATH DE Number: 3927137
zbMATH Keywords: direct summand
zbMATH Keywords: non-singular \(\aleph _ 0\)-continuous modules
zbMATH Keywords: regular ring
zbMATH Keywords: injective hull
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3927137