Noetherian domains which admit only finitely many star operations

DOI10.1016/j.jalgebra.2012.05.015zbMath1262.13041OpenAlexW2088583753MaRDI QIDQ1939292

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

Publication date: 4 March 2013

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2012.05.015

zbMATH Keywords

Noetherian domainstar operationdivisorial ideal

Mathematics Subject Classification ID

Integral domains (13G05)

Related Items (19)

Star, semistar and standard operations: a case study ⋮ Star operations on numerical semigroups: the multiplicity 3 case. ⋮ Power series over Noetherian domains, Nagata rings, and Kronecker function rings ⋮ 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 ⋮ The Number of Star Operations on Numerical Semigroups and on Related Integral Domains ⋮ When Two Principal Star Operations Are the Same ⋮ Multiplicative closure operations on ring extensions ⋮ The sets of star and semistar operations on semilocal Prüfer domains ⋮ Note on the divisoriality of domains of the form $k[[X^{p}, X^{q}]$, $k[X^{p}, X^{q}]$, $k[[X^{p}, X^{q}, X^{r}]]$, and $k[X^{p}, X^{q}, X^{r}]$] ⋮ Jaffard families and localizations of star operations ⋮ Star operations on numerical semigroups: antichains and explicit results ⋮ 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 ⋮ Finitely star regular domains ⋮ Star Operations on Numerical Semigroups

Cites Work

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• Warfield domains
• PID's with specified residue fields
• On the cardinality of star operations on a pseudo-valuation domain
• Structure on the set of closure operations of a commutative ring
• Reflexive domains
• 1-dimensional Cohen-Macaulay rings
• On the ubiquity of Gorenstein rings
• Integral Domains Which Admit at Most Two Star Operations
• Examples of star operations on integral domains
• Star-operations induced by overrings
• M-Canonical ideals in integral domains
• Integral domains in which each non‐zero ideal is divisorial

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