The product of divisibility groups \((G_1, \mathcal O _1)\times (G_2,\mathcal O_2)\) with \(G_1\) finitely generated

DOI10.1016/j.jalgebra.2007.07.020zbMath1145.13004OpenAlexW1993215208MaRDI QIDQ926851

Yves Lequain

Publication date: 21 May 2008

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2007.07.020

zbMATH Keywords

divisibility groups

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Ideals and multiplicative ideal theory in commutative rings (13A15) Extension theory of commutative rings (13B02) Ordered groups (06F15) Ordered groups (group-theoretic aspects) (20F60) General valuation theory for fields (12J20)

Related Items (1)

Realizations of semilocal ℓ-groups over k [ x ₁ , x ₂ ,… x _n ]

Cites Work

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• The weak approximation theorem for valuations
• The divisibility orders of \(\mathbb{Z}^n\)
• Extensions of semi-local rings sharing the same group of units
• Two counterexamples involving complete integral closure in finite- dimensional Prüfer domains
• Zero-dimensional branches of rank one on algebraic varieties
• Contribution à l'étude des groupes ordonnés
• Finitely generated groups of divisibility
• Integral Domains with Finitely Generated Groups of Divisibility
• Semi-Valuations and Groups of Divisibility

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