On Unique and Almost Unique Factorization of Complete Ideals

DOI10.2307/2374667zbMath0697.13007OpenAlexW2312862224MaRDI QIDQ3474746

Steven Dale Cutkosky

Publication date: 1989

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143720

zbMATH Keywords

UFDclass grouprational singularityunique factorizationcomplete idealssemifactorialitycondition (N)

Mathematics Subject Classification ID

Singularities of surfaces or higher-dimensional varieties (14J17) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15)

Related Items (14)

Cohomological characterizations of smoothness and the case of rational surface singularities ⋮ Factorization of complete ideals in normal birational extensions in dimension two ⋮ A new characterization of rational surface singularities ⋮ Integral closedness of \(MI\) and the formula of Hoskin and Deligne for finitely supported complete ideals ⋮ Factorization of complete ideals ⋮ Integral closure and other operations on monomial ideals ⋮ A local version of some results of zariski ⋮ Quasi-one-fibered and projectively full ideals in 2-dimensional Muhly rational singularities ⋮ Blowups in tame monomial ideals ⋮ Discrete valuations centered on local domains ⋮ Integrally closed and componentwise linear ideals ⋮ Graded rings associated with contracted ideals ⋮ Some results relating to adjacent ideals in dimension two ⋮ Unique factorization of *-products of one-fibered monomial ideals

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