A category equivalence between homogeneous completely decomposable Abelian groups and modules over principal ideal domains

DOI10.1016/S0022-4049(00)00049-9zbMath0985.20045OpenAlexW2080262389MaRDI QIDQ5939826

Lutz H. Strüngmann

Publication date: 20 February 2002

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-4049(00)00049-9

zbMATH Keywords

free modulestorsion-free Abelian groupscategory equivalenceshomogeneous completely decomposable groupsprincipal ideal domainsrational groupsrepresentations of finite posets

Mathematics Subject Classification ID

Projective and free modules and ideals in commutative rings (13C10) Representations of quivers and partially ordered sets (16G20) Homological and categorical methods for abelian groups (20K40) Direct sums, direct products, etc. for abelian groups (20K25) Torsion-free groups, finite rank (20K15)

Cites Work

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• The endomorphism ring of an Abelian torsionfree homogeneous separable group
• Gauß' theorem for two submodules
• Homomorphisms and duality for torsion-free groups
• Stacked bases for modules over principal ideal domains
• Classification of modules with two distinguished pure submodules and bounded quotients
• STACKED BASES FOR HOMOGENEOUS COMPLETELY DECOMPOSABLE GROUPS
• Generalizations of the Stacked Bases Theorem
• Representations over PID’s with three distinguished submodules

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