The divisibility orders of \(\mathbb{Z}^n\)

DOI10.1006/jabr.1998.7625zbMath0940.12006OpenAlexW2006118520MaRDI QIDQ1283955

Yves Lequain, Ada Maria de Souza Doering

Publication date: 24 July 2000

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

Full work available at URL: https://doi.org/10.1006/jabr.1998.7625

zbMATH Keywords

ordered groupsultrafiltervaluation ringgroup of divisibilitydivisibility orders

Mathematics Subject Classification ID

Ordered groups (06F15) Ordered groups (group-theoretic aspects) (20F60) Divisibility and factorizations in commutative rings (13A05) General valuation theory for fields (12J20)

Related Items

The product of divisibility groups \((G_1, \mathcal O _1)\times (G_2,\mathcal O_2)\) with \(G_1\) finitely generated ⋮ The weak approximation theorem for valuations ⋮ Extensions of semi-local rings sharing the same group of units

Cites Work

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• Valuations and semi-valuations of graded domains
• The weak approximation theorem for valuations
• Two counterexamples involving complete integral closure in finite- dimensional Prüfer domains
• Contribution à l'étude des groupes ordonnés
• Finitely generated groups of divisibility
• Semi-Valuations and Groups of Divisibility