On the unions of ascending chains of direct sums of ideals of \(h\)-local Prüfer domains

DOI10.1142/S1005386711000629zbMATH Open1294.13014arXiv1112.0600MaRDI QIDQ2876996

J. E. Macías-Díaz

Publication date: 21 August 2014

Published in: Algebra Colloquium (Search for Journal in Brave)

Abstract: In this work, we investigate conditions under which unions of ascending chains of modules which are isomorphic to direct sums of ideals of an integral domain are again isomorphic to direct sums of ideals. We obtain generalizations of the Pontryagin-Hill theorems for modules which are direct sums of ideals of h-local Pr"{u}fer domains. Particularly, we prove that a torsion-free module over a Dedekind domain with a countable number of maximal ideals is isomorphic to a direct sum of ideals if it is the union of a countable ascending chain of pure submodules which are isomorphic to direct sums of ideals.

Full work available at URL: https://arxiv.org/abs/1112.0600

zbMATH Keywords

Pontryagin-Hill theoremsdirect sums of ideals\(h\)-local Prüfer domainsascending chains of modulesbalancedness of modules

Mathematics Subject Classification ID

Integral domains (13G05) Structure, classification theorems for modules and ideals in commutative rings (13C05) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Other special types of modules and ideals in commutative rings (13C13)

Cites Work

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ON INTEGRAL DOMAINS IN WHICH EVERY ASCENDING CHAIN ON PRINCIPAL IDEALS IS S-STATIONARY

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