Coseparable torsionfree Abelian groups
type: Item
instance of: scholarly article
title: Coseparable torsionfree Abelian groups
zbMATH Open document ID: 0568.20054
DOI: 10.1007/BF01270482
author: Claudia Metelli
published in: Archiv der Mathematik
publication date: 1985-01-01T00:00:00Z
review text: The author develops a concept of coseparability, dual to separability, for torsion-free abelian groups of arbitrary nonmeasurable rank and establishes several important properties. A group G is coseparable if every pure subgroup of finite corank contains a summand of G which has a completely decomposable finite rank complement. Vector groups are coseparable, but not vice versa. Finite rank coseparable groups are completely decomposable, but countable rank ones need not be. Coseparability is closed under products and summands, but not sums.
Mathematics Subject Classification ID: 20K20
Mathematics Subject Classification ID: 20K27
zbMATH DE Number: 3906752
zbMATH Keywords: coseparability
zbMATH Keywords: torsion-free abelian groups
zbMATH Keywords: pure subgroup of finite corank
zbMATH Keywords: completely decomposable finite rank complement
zbMATH Keywords: Vector groups
zbMATH Keywords: coseparable groups
reviewed by: Phillip Schultz
MaRDI profile type: Publication
cites work: A Class of Torsion-Free Abelian Groups of Finite Rank
cites work: Q5510862
cites work: Q5673086
cites work: Separability of torsion free groups and a problem of J.H.C. Whitehead
cites work: Q5831361
description: scientific article; zbMATH DE number 3906752