Numerical characterizations of some integral domains

DOI10.1007/S00605-010-0205-0zbMath1228.13023OpenAlexW2055964828MaRDI QIDQ646618

Ali Jaballah

Publication date: 17 November 2011

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-010-0205-0

zbMATH Keywords

Dedekind domainNoetherian ringPrüfer domainsAntichainChainIntegral domainIntegrally closedOverringQQR-domainQR-domainQuotients and localizationsTreeValuation domains

Mathematics Subject Classification ID

Trees (05C05) Integral closure of commutative rings and ideals (13B22) Commutative Noetherian rings and modules (13E05) Valuations and their generalizations for commutative rings (13A18) Integral domains (13G05) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Rings of fractions and localization for commutative rings (13B30)

Related Items (5)

A FINITENESS CONDITION ON QUASI-LOCAL OVERRINGS OF A CLASS OF PINCHED DOMAINS ⋮ Graph theoretic characterizations of maximal non-valuation subrings of a field ⋮ The number of intermediate rings in FIP extension of integral domains ⋮ MAXIMAL NON-PRÜFER AND MAXIMAL NON-INTEGRALLY CLOSED SUBRINGS OF A FIELD ⋮ A finiteness condition on the set of overrings of some classes of integral domains

Cites Work

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• The number of overrings of an integrally closed domain
• Residually algebraic pairs of rings
• Pairs of domains where all intermediate domains are Jaffard
• Intersections of quotient rings of an integral domain
• The spectrum of a ring as a partially ordered set
• Ring extensions with some finiteness conditions on the set of intermediate rings
• A lower bound for the number of intermediary rings
• Some finiteness conditions on the set of overrings of an integral domain
• Overrings of Commutative Rings. II. Integrally Closed Overrings

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