A counterexample for a conjecture about the catenarity of polynomial rings.

DOI10.1006/jabr.2001.9046zbMath1041.13008OpenAlexW1966929221WikidataQ123025263 ScholiaQ123025263MaRDI QIDQ1599096

Mabrouk Ben Nasr, Noômen Jarboui

Publication date: 2 July 2002

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

Full work available at URL: https://doi.org/10.1006/jabr.2001.9046

zbMATH Keywords

altitude formulanon-Noetherian ringstrong S-domainnon catenary ring

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15) Chain conditions, finiteness conditions in commutative ring theory (13E99)

Related Items (8)

A question about saturated chains of primes in Serre conjecture rings ⋮ On universally catenarian pairs ⋮ Universally catenarian domains of the type \(A + I\) ⋮ A note on maximal non-Noetherian subrings of a domain ⋮ An answer to a Dobbs conjecture about treed domains ⋮ About the spectrum of Nagata rings ⋮ ON MAXIMAL NON-UNIVERSALLY CATENARIAN SUBRINGS ⋮ On questions related to stably strong S-domains

Cites Work

• Strong S-domains
• Universally catenarian integral domains
• Construction B, I, D et anneaux localement ou residuellement de Jaffard. (B, I, D construction and locally or residually Jaffard rings)
• Couples d'anneaux partageant un idéal. (Couples of rings sharing an ideal)
• Chains of prime ideals in polynomial rings
• On Quasi-Unmixed Local Domains, the Altitude Formula, and the Chain Condition for Prime Ideals (II)
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