A Remak-Krull-Schmidt Class of Torsion-Free Abelian Groups

DOI10.1007/978-3-319-51718-6_3zbMath1436.20098OpenAlexW2621078618MaRDI QIDQ3298246

Ebru Solak, David M. Arnold, Otto Mutzbauer, Adolf Mader

Publication date: 14 July 2020

Published in: Groups, Modules, and Model Theory - Surveys and Recent Developments (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-51718-6_3

zbMATH Keywords

indecomposabilityalmost completely decomposable groupbounded representation typeRemak-Krull-Schmidt

Mathematics Subject Classification ID

Representation type (finite, tame, wild, etc.) of associative algebras (16G60) Extensions of abelian groups (20K35) Direct sums, direct products, etc. for abelian groups (20K25) Torsion-free groups, finite rank (20K15)

Cites Work

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• The class of \((1,3)\)-groups with homocyclic regulator quotient of exponent \(p^4\) has bounded representation type.
• Almost completely decomposable groups and unbounded representation type.
• Representations of finite posets over the ring of integers modulo a prime power
• Nearly isomorphic torsion free abelian groups
• Abelian groups and representations of finite partially ordered sets
• Classification of a class of torsion-free abelian groups
• Indecomposable (1,3)-Groups and a matrix problem
• Almost Completely Decomposable Torsion Free Abelian Groups

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