On p-local Abelian groups with decomposition bases
type: Item
instance of: scholarly article
title: On p-local Abelian groups with decomposition bases
zbMATH Open document ID: 0655.20035
DOI: 10.1007/BF01180687
published in: Mathematische Zeitschrift
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174079
review text: A study is presented of those p-local abelian groups G which possess a nice decomposition basis with cokernel an S-group, and we use the theory of cotorsion groups and techniques which were successful in characterizing the structure of summands of S-groups to prove that such a group must decompose into a direct sum of a Warfield group and an S- group. From this characterization of these groups, we are able to show that a summand of a direct sum of a Warfield group and an S-group is itself a direct sum of a Warfield group and an S-group, and this extends the structure theory of Warfield groups and of S-groups to this larger class of groups. Finally, another application of the main result is given which describes this class of groups as those isotype subgroups of p- local Warfield groups with cokernel a coproduct of countable torsion groups under the coset valuation.
Mathematics Subject Classification ID: 20K21
Mathematics Subject Classification ID: 20K10
Mathematics Subject Classification ID: 20K25
Mathematics Subject Classification ID: 20K30
Mathematics Subject Classification ID: 20K27
zbMATH DE Number: 4069193
zbMATH Keywords: p-local abelian groups
zbMATH Keywords: decomposition basis
zbMATH Keywords: cotorsion groups
zbMATH Keywords: summands of S-groups
zbMATH Keywords: direct sum
zbMATH Keywords: Warfield groups
zbMATH Keywords: isotype subgroups of p-local Warfield groups
zbMATH Keywords: coproduct of countable torsion groups
zbMATH Keywords: coset valuation
author: Mark T. Lane
MaRDI profile type: Publication
cites work: Global Azumaya theorems in additive categories
cites work: Q5609457
cites work: On the Structure of Abelian p-Groups
cites work: Axiom 3 Modules
cites work: Q4206946
cites work: Global Warfield Groups
cites work: Existence Theorems for Warfield Groups
cites work: S-Groups Revisited
cites work: Projective modules
cites work: A New Characterization for p-Local Balanced Projective Groups
cites work: Isotype Submodules of p-Local Balanced Projective Groups
cites work: A Classification Theorem for Abelian p-Groups
cites work: Classification Theory of Abelian Groups. I: Balanced Projectives
cites work: A Projective Characterization for SKT-modules
description: scientific article; zbMATH DE number 4069193