M-Canonical ideals in integral domains

DOI10.1080/00927879808826325zbMath0920.13001OpenAlexW2087077255MaRDI QIDQ4212558

James A. Huckaba, Ira J. Papick, William J. Heinzer

Publication date: 13 September 1999

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

Full work available at URL: https://doi.org/10.1080/00927879808826325

zbMATH Keywords

valuation domainPrüfer domain\(m\)-canonical ideal

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 (30)

A Characterization of Valuation Domains via m-Canonical Ideals ⋮ Prüferv-Multiplication Domains andw-Multiplicative Canonical Ideals ⋮ Almost maximal prüfer domains ⋮ Factoring ideals in Prüfer domains ⋮ Star stable domains ⋮ Towards a classification of stable semistar operations on a Prüfer domain ⋮ A characterization of local Noetherian domains which admit only finitely many star operations: the infinite residue field case ⋮ Decompositions of ideals into irreducible ideals in numerical semigroups. ⋮ Noetherian domains which admit only finitely many star operations ⋮ Projective star operations on polynomial rings over a field ⋮ Homological dimensions of the amalgamated duplication of a ring along a pure ideal ⋮ Star operations on Prüfer \(v\)-multiplication domains ⋮ When Two Principal Star Operations Are the Same ⋮ Multiplicative closure operations on ring extensions ⋮ Multiplicative canonical ideals of ring extensions ⋮ The amalgamated duplication of a ring along a multiplicative-canonical ideal ⋮ Jaffard families and localizations of star operations ⋮ Unnamed Item ⋮ AN AMALGAMATED DUPLICATION OF A RING ALONG AN IDEAL: THE BASIC PROPERTIES ⋮ w-Divisoriality in Polynomial Rings ⋮ Local rings of minimal length ⋮ Star Operations on Overrings and Semistar Operations ⋮ Some classification of certain integral domains via conductor overrings and semistar operations ⋮ Integral Domains Which Admit at Most Two Star Operations ⋮ Star operations on modules ⋮ Asymptotic for the number of star operations on one-dimensional Noetherian domains ⋮ Integrally Closed Domains with Only Finitely Many Star Operations ⋮ Star Operations on Numerical Semigroups ⋮ Some results on presemistar operations ⋮ INTEGRAL DOMAINS WITH FINITELY MANY STAR OPERATIONS OF FINITE TYPE

Cites Work

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• The radical trace property
• Integral domains in which each t-ideal is divisorial
• Warfield domains
• Globalizing local properties of Prüfer domains
• Reflexive domains
• 1-dimensional Cohen-Macaulay rings
• On the ubiquity of Gorenstein rings
• Integral domains in which each non‐zero ideal is divisorial
• A Note on Analytically Unramified Local Rings

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