Rings with a theory of greatest common divisors

DOI10.1007/BF02678019zbMath0901.13001MaRDI QIDQ1382642

Friedemann Lucius

Publication date: 13 May 1998

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/156364

zbMATH Keywords

divisibilityintegral closure*-ideal theory\(\nu\)-domainring with gcd-theory

Mathematics Subject Classification ID

Ideals and multiplicative ideal theory in commutative rings (13A15) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Euclidean rings and generalizations (13F07) Divisibility and factorizations in commutative rings (13A05)

Related Items (8)

Almost-Schreier Domains ⋮ Kronecker Function Rings and Generalized Integral Closures ⋮ \(\star\)-super potent domains ⋮ On the transfer of some $t-$locally properties ⋮ Anneaux à diviseurs et anneaux de Krull (une approche constructive) ⋮ Realization and GCD-existence theorem for generalized polynomials ⋮ Characterization of Prüfer-Like Monoids and Domains by GCD-Theories ⋮ PRÜFER ⋆-MULTIPLICATION DOMAINS AND SEMISTAR OPERATIONS

Cites Work

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• Divisors of finite character
• n-generator ideals in Prüfer domains
• Prüfer v-multiplication domains and the ring \(R[X_{N_ v}\)]
• Idéaux divisoriels d'un anneau de polynômes
• On Pruefer v-multiplication domains
• Quasi-divisor theories and generalizations of Krull domains
• Beiträge zur Arithmetik kommutativer Integritätsbereiche. II. \(v\)- Ideale und vollständig ganz abgeschlossene Integritätsbereiche
• Untersuchungen über Teilbarkeitseigenschaften in Körpern.

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