Krull Dimension in Power Series Ring Over an Almost Pseudo-Valuation Domain

DOI10.1080/00927870903107957zbMath1242.13006OpenAlexW2026106109MaRDI QIDQ3162832

Ali Benhissi, Mohamed Khalifa

Publication date: 22 October 2010

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

Full work available at URL: https://doi.org/10.1080/00927870903107957

zbMATH Keywords

Krull dimensionpower series ringAPVD

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Ideals and multiplicative ideal theory in commutative rings (13A15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15) Formal power series rings (13F25)

Related Items

Jump of a domain and spectrally balanced domains ⋮ SFT-stability and Krull dimension in power series rings over an almost pseudo-valuation domain ⋮ Note on valuative dimension in power series rings

Cites Work

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• Conducive integral domains
• SFT stability via power series extension over Prüfer domains
• Power series rings over globalized pseudo-valuation domains
• Couples d'anneaux partageant un idéal. (Couples of rings sharing an ideal)
• Catenarity of formal power series rings over a pullback
• A localization of a power series ring over a valuation domain
• The SFT property does not imply finite dimension for power series rings.
• Sur la catenarite des anneaux de series formelles sur un anneau de prüfer
• Anti-archimedean rings and power series rings
• POWERFUL IDEALS, STRONGLY PRIMARY IDEALS, ALMOST PSEUDO-VALUATION DOMAINS, AND CONDUCIVE DOMAINS

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