A note on the direct limit of increasing sequences of completely decomposable modules over integral domains

zbMATH Open1243.13007arXiv1112.0608MaRDI QIDQ2901438

Jorge Eduardo Macías-Díaz

Publication date: 20 July 2012

Published in: International Journal of Algebra (Search for Journal in Brave)

Abstract: In this note, we establish conditions under which the union of an increasing sequence of completely decomposable modules over domains are again completely decomposable. In our investigation, the condition of purity of modules is crucial. In fact, the main result reported in this work states that a module is completely decomposable when it is the union of a countable, ascending chain of completely decomposable, pure submodules, providing thus a generalization of Hill's criterion of freeness from abelian group theory.

Full work available at URL: https://arxiv.org/abs/1112.0608

zbMATH Keywords

integral domainscompletely decomposable modulesPontryagin-Hill theoremsincreasing sequences of modulespurity of modules

Mathematics Subject Classification ID

Projective and free modules and ideals in commutative rings (13C10) Structure, classification theorems for modules and ideals in commutative rings (13C05) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (3)

Title not available (Why is that?) ⋮ CHAINS OF PROJECTIVE MODULES ⋮ STACKED BASES FOR COUNTABLE HOMOGENEOUS COMPLETELY DECOMPOSABLE GROUPS

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