Semigroup Rings as Weakly Factorial Domains

DOI10.1080/00927870802502746zbMath1200.13003OpenAlexW2144459194MaRDI QIDQ3644353

Gyu Whan Chang

Publication date: 4 November 2009

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

Full work available at URL: https://doi.org/10.1080/00927870802502746

zbMATH Keywords

GCD-domainsemigroup ringweakly factorial domainGCD-semigroup

Mathematics Subject Classification ID

Integral domains (13G05) Ideals and multiplicative ideal theory in commutative rings (13A15) Semigroup rings, multiplicative semigroups of rings (20M25) Arithmetic rings and other special commutative rings (13F99)

Related Items (8)

The set of distances in seminormal weakly Krull monoids ⋮ Semigroup rings as weakly Krull domains ⋮ Semigroup rings as weakly factorial domains, II ⋮ A characterization of weakly Krull monoid algebras ⋮ Weakly factorial property of a generalized Rees ring \(D[X,d/X\)] ⋮ Generalized Krull domains and the composite semigroup ring \(D+E[\Gamma^{\ast}\)] ⋮ Arithmetic of seminormal weakly Krull monoids and domains ⋮ Unique factorization property of non-unique factorization domains

Cites Work

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• On primary factorizations
• Divisibility properties in semigroup rings
• \(t\)-linked extensions, the \(t\)-class group, and Nagata's theorem
• Weakly Krull and related domains of the form \(D+M, A+XB[X\) and \(A+X^2B[X]\)]
• Homogeneous splitting sets of a graded integral domain
• On t-invertibility II
• On divisorial ideals in polynomial rings over mori domains
• Umt-domains and domains with prüfer integral closure
• Prime Ideals in GCD-Domains

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