Six notes on chains of prime ideals

DOI10.1007/BF01761487zbMath0483.13002OpenAlexW2041271916MaRDI QIDQ1163060

Louis J. jun. Ratliff

Publication date: 1982

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01761487

zbMATH Keywords

heightJacobson radicalNoetherianHenselian local ringcatenary ringlocal domainchain condition for prime idealsCi-ringDi-ringHi- ringintegral extension domains

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Commutative Noetherian rings and modules (13E05) Polynomials over commutative rings (13B25) Ideals and multiplicative ideal theory in commutative rings (13A15) Extension theory of commutative rings (13B02) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15) Chain conditions, finiteness conditions in commutative ring theory (13E99)

Cites Work

• Notes on three integral dependence theorems
• Four notes on GB-rings
• A non-catenary, normal, local domain
• Four notes on saturated chains of prime ideals
• Going-between rings and contractions of saturated chains of prime ideals
• A particular class of regular domains
• Chain conjectures in ring theory. An exposition of conjectures on catenary chains
• Piecewise catenarian and going-between rings
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Séconde partie)
• Note on Simple Integral Extension Domains and Maximal Chains of Prime Ideals
• On maximal ideals and simple integral extension rings
• Notes on Local Integral Extension Domains
• Examples of Noncatenary Rings
• On Quasi-Unmixed Local Domains, the Altitude Formula, and the Chain Condition for Prime Ideals, (I)
• On Quasi-Unmixed Local Domains, the Altitude Formula, and the Chain Condition for Prime Ideals (II)
• Characterizations of Catenary Rings
• Prime ideals and integral dependence
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