Torsion-free E-modules
type: Item
instance of: scholarly article
title: Torsion-free E-modules
zbMATH Open document ID: 0639.13010
DOI: 10.1016/0021-8693(88)90266-9
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: A module M over a unital commutative ring R is called an E-module if every additive homomorphism from R into M is a module homomorphism. While this definition seems very specialized, E-modules play an important role in the study of torsion-free abelian groups. In this paper the authors characterize finite rank E-modules M over finite rank torsion-free rings R. They first reduce the problem to the case in which R is an integrally closed subring of an algebraic number field F and M is semi-local, and then characterize M in terms of the Galois structure of F over \({\mathbb{Q}}\).
Mathematics Subject Classification ID: 13C13
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 20K20
Mathematics Subject Classification ID: 20K30
zbMATH DE Number: 4042045
zbMATH Keywords: Galois closure
zbMATH Keywords: torsion-free abelian groups
zbMATH Keywords: finite rank E-modules
author: Adolf Mader
author: Charles Vinsonhaler
reviewed by: Phillip Schultz
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90266-9
OpenAlex ID: W2005340012
cites work: Torsion-free rings
cites work: Q5726743
cites work: Unital rings whose additive endomorphisms commute
cites work: Q5612629
cites work: Q3661679
cites work: The endomorphism ring of the additive group of a ring
description: scientific article; zbMATH DE number 4042045