Generating an injective class of torsion-free Abelian groups
type: Item
instance of: scholarly article
title: Generating an injective class of torsion-free Abelian groups
zbMATH Open document ID: 0681.20035
DOI: 10.1007/BF02170063
published in: Acta Mathematica Hungarica
publication date: 1989-01-01T00:00:00Z
review text: Let \(\Lambda\) be a set of torsionfree abelian groups of finite rank. The class \({\mathcal C}^ 0(\Lambda)\) consists of those torsionfree finite rank groups C such that each \(A\in \Lambda\) is injective with respect to any pure exact sequence E: \(0\to B\to C\to K\to 0\). Further, \({\mathcal I}{\mathcal C}^ 0(\Lambda)\) denotes the class of all torsionfree finite rank groups which are injective with respect to all pure exact sequences E with C from \({\mathcal C}^ 0(\Lambda)\). The author characterizes the classes \({\mathcal C}^ 0(\Lambda)\) and \({\mathcal I}{\mathcal C}^ 0(\Lambda)\) in the case when \(\Lambda\) consists of torsionfree groups of rank one. In the last part the dual (projective) case is considered.
Mathematics Subject Classification ID: 20K15
Mathematics Subject Classification ID: 20K40
zbMATH DE Number: 4114891
zbMATH Keywords: injective class
zbMATH Keywords: torsionfree abelian groups of finite rank
zbMATH Keywords: pure exact sequence
Wikidata QID: Q114233876
author: Pat Goeters
reviewed by: Ladislav Bican
MaRDI profile type: Publication
cites work: Quasi-Pure Injective and Projective Torsion-Free Abelian Groups of Finite Rank
cites work: When do two groups always have isomorphic extension groups?
cites work: Projective classes of torsion free Abelian groups
description: scientific article; zbMATH DE number 4114891