Most abelian \(p\)-groups are determined by the Jacobson radical of their endomorphism rings
type: Item
instance of: scholarly article
title: Most abelian \(p\)-groups are determined by the Jacobson radical of their endomorphism rings
zbMATH Open document ID: 0811.20046
DOI: 10.1007/BF02572332
author: Jutta Hausen
author: Cheryl E. Praeger
author: Phillip Schultz
published in: Mathematische Zeitschrift
publication date: 1994-12-21T00:00:00Z
full work available at URL: https://eudml.org/doc/174661
review text: The torsion radical of a ring is the ideal consisting of all torsion elements in its Jacobson radical. It is shown that an abelian \(p\)-group with unbounded basic subgroup is determined by the torsion radical of its endomorphism ring. For \(p\)-groups which are bounded modulo their maximal divisible subgroups, the theorem fails.
reviewed by: Jutta Hausen
Mathematics Subject Classification ID: 20K30
Mathematics Subject Classification ID: 20K10
Mathematics Subject Classification ID: 16N20
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 20K27
zbMATH DE Number: 704928
zbMATH Keywords: torsion radical
zbMATH Keywords: torsion elements
zbMATH Keywords: Jacobson radical
zbMATH Keywords: unbounded basic subgroup
zbMATH Keywords: endomorphism ring
zbMATH Keywords: \(p\)-groups
zbMATH Keywords: maximal divisible subgroups
Wikidata QID: Q56988281
MaRDI profile type: Publication
cites work: Automorphism rings of primary abelian operator groups
cites work: On the Jacobson Radical of Some Endomorphism Rings
cites work: Quasi-regular ideals of some endomorphism rings
cites work: Characterization of the primary abelian groups, bounded modulo the divisible subgroup, by the radical of their endomorphism rings
cites work: Some Results on Abelian Groups
cites work: Q4025961
cites work: Primary abelian groups as modules over their endomorphism rings
OpenAlex ID: W2058057634
description: scientific article; zbMATH DE number 704928