Finitely generated groups of divisibility

DOI10.1090/conm/008/653184zbMath0482.13001OpenAlexW4243352374MaRDI QIDQ3939909

Joe L. Mott, Bruce Glastad

Publication date: 1982

Published in: Ordered fields and real algebraic geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/conm/008/653184

zbMATH Keywords

valuation ringBezout domainorder structure of group of divisibility of an integral domain

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Integral domains (13G05) Valuation rings (13F30) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Ordered groups (06F15) Divisibility and factorizations in commutative rings (13A05)

Related Items (11)

Finite factorization domains ⋮ The product of divisibility groups \((G_1, \mathcal O _1)\times (G_2,\mathcal O_2)\) with \(G_1\) finitely generated ⋮ Cohen-Kaplansky domains: Integral domains with a finite number of irreducible elements ⋮ Integral Domains with Finitely Generated Groups of Divisibility ⋮ Commutative rings with finitely generated monoids of fractional ideals ⋮ The weak approximation theorem for valuations ⋮ The divisibility orders of \(\mathbb{Z}^n\) ⋮ Realizations of semilocal ℓ-groups over k [ x ₁ , x ₂ ,… x _n ] ⋮ Atoms in quasilocal integral domains and Cohen–Kaplansky domains ⋮ Factorization in integral domains ⋮ Extensions of semi-local rings sharing the same group of units

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