Determination of a class of countable-rank, torsion-free Abelian groups by their endomorphism rings.
type: Item
instance of: scholarly article
title: Determination of a class of countable-rank, torsion-free Abelian groups by their endomorphism rings.
zbMATH Open document ID: 1160.20053
author: Ekaterina Blagoveshchenskaya
published in: Journal of Mathematical Sciences (New York)
publication date: 2008-10-28T00:00:00Z
review text: It has been previously shown that if \(X\) and \(Y\) are block-rigid, almost completely decomposable torsion-free Abelian groups of ring type and finite rank with cyclic regulator quotient, then \(X\) and \(Y\) are near isomorphic if and only if \(\text{End}(X)\) and \(\text{End}(Y)\) are isomorphic. The current work extends this result to block-rigid, `local' almost completely decomposable torsion-free Abelian groups of ring type and `countable' rank with cyclic regulator quotient. A block-rigid almost completely decomposable group with cyclic regulator quotient is a torsion-free Abelian group \(X\) containing a uniquely determined, completely decomposable, fully invariant subgroup \(A=R(X)\) called its regulator such that \(X/A\) is a finite cyclic group. The definition of a local almost completely decomposable group with cyclic regulator quotient is more complicated, but is included in the paper under review.
Mathematics Subject Classification ID: 20K20
Mathematics Subject Classification ID: 20K30
Mathematics Subject Classification ID: 16S50
zbMATH DE Number: 5358195
zbMATH Keywords: endomorphism rings
zbMATH Keywords: countable rank Abelian groups
zbMATH Keywords: torsion-free Abelian groups
zbMATH Keywords: almost completely decomposable block rigid torsion-free Abelian groups
zbMATH Keywords: regulator quotients
reviewed by: Ross P. Abraham
MaRDI profile type: Publication
full work available at URL: s10958-008-9084-5
OpenAlex ID: W2090941602
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DOI: 10.1007/S10958-008-9084-5
description: scientific article; zbMATH DE number 5358195