Pseudo-almost valuation domains are quasilocal going-down domains, but not conversely

DOI10.1007/s12215-008-0006-7zbMath1164.13003OpenAlexW1978521973MaRDI QIDQ931337

David E. Dobbs

Publication date: 25 June 2008

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12215-008-0006-7

zbMATH Keywords

Krull dimension\(D+M\) constructionDivide domainGoing down domainPrime idealPseudo-almost valuation domainQuasilocalRoot extensionSeminormalValuation overring

Mathematics Subject Classification ID

Integral domains (13G05) Ideals and multiplicative ideal theory in commutative rings (13A15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (3)

On a New Class of Integral Domains with the Portable Property ⋮ Unnamed Item ⋮ Trivial extensions satisfying certain valuation-like properties

Cites Work

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• Divided rings and going-down
• Inside factorial monoids and integral domains
• On Pseudo-Almost Valuation Domains
• POWERFUL IDEALS, STRONGLY PRIMARY IDEALS, ALMOST PSEUDO-VALUATION DOMAINS, AND CONDUCIVE DOMAINS
• On Going Down For Simple Overrings II
• On Going-Down for Simple Overrings. III

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