VALUATIVE DOMAINS

DOI10.1142/S021949881000377XzbMath1191.13009OpenAlexW4235127813MaRDI QIDQ5305534

Thomas G. Lucas, Paul-Jean Cahen, David E. Dobbs

Publication date: 22 March 2010

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s021949881000377x

zbMATH Keywords

valuation domainmaximal idealprime idealBézout domainintegralitypseudo-valuation domainminimal ring extension\(i\)-domain

Mathematics Subject Classification ID

Integral domains (13G05) Ideals and multiplicative ideal theory in commutative rings (13A15) Integral dependence in commutative rings; going up, going down (13B21) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Rings of fractions and localization for commutative rings (13B30) Commutative ring extensions and related topics (13B99)

Related Items (9)

Pointwise minimal extensions ⋮ Valuative rings ⋮ Boolean FIP ring extensions ⋮ Paul-Jean Cahen (1946–2019) ⋮ Valuative Marot Rings ⋮ Δ-Extension of rings and invariance properties of ring extension under group action ⋮ Ring extensions of length two ⋮ On the existence of maximal subrings in commutative noetherian rings ⋮ FINITELY VALUATIVE DOMAINS

Cites Work

• Unnamed Item
• Unnamed Item
• A classification of the minimal ring extensions of certain commutative rings
• Topologically defined classes of commutative rings
• Pseudo-valuation domains
• Overrings of Prüfer domains. II
• Homomorphismes minimaux d'anneaux
• The spectrum of a ring as a partially ordered set
• On minimal overrings of a noetherian domain
• Ascent and descent of going-down rings for integral extensions
• Pairs of Rings with the Same Prime Ideals
• Minimal Overrings of an Integrally Closed Domain
• On Going Down For Simple Overrings II

This page was built for publication: VALUATIVE DOMAINS