Integral Domains Which Admit at Most Two Star Operations

DOI10.1080/00927872.2010.480956zbMath1223.13002OpenAlexW2166247294MaRDI QIDQ3090107

Mi Hee Park, Abdeslam Mimouni, Evan G. jun. Houston

Publication date: 26 August 2011

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

Full work available at URL: https://doi.org/10.1080/00927872.2010.480956

zbMATH Keywords

Prüfer domainKrull domainintegral domainalmost Dedekind domainPVDdivisorial ideal\(h\)-local domainnumber of star operations

Mathematics Subject Classification ID

Ideals and multiplicative ideal theory in commutative rings (13A15) Valuation rings (13F30) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (24)

Star, semistar and standard operations: a case study ⋮ Radical semistar operations ⋮ Topological properties of localizations, flat overrings and sublocalizations ⋮ Star operations on numerical semigroups: the multiplicity 3 case. ⋮ Unnamed Item ⋮ Star operations on overrings of Noetherian domains ⋮ A characterization of local Noetherian domains which admit only finitely many star operations: the infinite residue field case ⋮ Noetherian domains which admit only finitely many star operations ⋮ The Number of Star Operations on Numerical Semigroups and on Related Integral Domains ⋮ Star operations on Prüfer \(v\)-multiplication domains ⋮ When Two Principal Star Operations Are the Same ⋮ On the cardinality of stable star operations of finite type on an integral domain ⋮ The sets of star and semistar operations on semilocal Prüfer domains ⋮ Jaffard families and localizations of star operations ⋮ Star operations on numerical semigroups: antichains and explicit results ⋮ Locally pseudo-valuation domains with only finitely many star operations ⋮ Star operations on Kunz domains ⋮ Star operations on overrings of Prüfer domains ⋮ Asymptotic for the number of star operations on one-dimensional Noetherian domains ⋮ On some classes of integral domains with finitely many star operations of finite type ⋮ Integrally Closed Domains with Only Finitely Many Star Operations ⋮ Finitely star regular domains ⋮ Star Operations on Numerical Semigroups ⋮ INTEGRAL DOMAINS WITH FINITELY MANY STAR OPERATIONS OF FINITE TYPE

Cites Work

• Unnamed Item
• Unnamed Item
• Warfield domains
• Pseudo-valuation domains
• Globalizing local properties of Prüfer domains
• Factoring ideals in Prüfer domains
• Reflexive domains
• On the ubiquity of Gorenstein rings
• Examples of star operations on integral domains
• Star-operations induced by overrings
• M-Canonical ideals in integral domains
• Integral Domains in Which Each Ideal Is aW-Ideal
• Integral domains in which each non‐zero ideal is divisorial

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