Prüfer \(v\)-multiplication domains and related domains of the form \(D+D_S[\varGamma ^{*}]\)

DOI10.1016/j.jalgebra.2010.03.010zbMath1192.13002OpenAlexW2313298070MaRDI QIDQ975113

Jung Wook Lim, Gyu Whan Chang, Byung Gyun Kang

Publication date: 8 June 2010

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2010.03.010

zbMATH Keywords

P\(v\)MD\(D+D_S[\Gamma^*\)]\(t\)-splitting settorsion-free grading monoid \(\Gamma\) with \(\Gamma\cap-\Gamma=\{0\}\)

Mathematics Subject Classification ID

Graded rings (13A02) Integral domains (13G05) Ideals and multiplicative ideal theory in commutative rings (13A15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (18)

The Schreier property and the composite semigroup ring A + B[Γ*] ⋮ Numerical Semigroup Rings and Almost Prüferv-Multiplication Domains ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Graded integral domains which are UMT-domains ⋮ Semigroup rings as almost Prüfer \(v\)-multiplication domains ⋮ The construction D + XD _S [ X and G -Prüfer domains] ⋮ On locally AGCD domains ⋮ UMT-domains: A Survey ⋮ Graded integral domains and Nagata rings ⋮ Graded integral domains in which each nonzero homogeneous t-ideal is divisorial ⋮ The \(D + E[\varGamma^*\) construction from Prüfer domains and GCD-domains] ⋮ WHEN ARE GRADED INTEGRAL DOMAINS ALMOST GCD-DOMAINS ⋮ Generalized Krull domains and the composite semigroup ring \(D+E[\Gamma^{\ast}\)] ⋮ Graded Prüfer domains with Clifford homogeneous class semigroups ⋮ Generalized Krull Semigroup Rings ⋮ CHARACTERIZATIONS OF GRADED PRÜFER ⋆-MULTIPLICATION DOMAINS ⋮ Almost Prüferv-Multiplication Domains and Related Domains of the FormD + D_S[Γ*]

Cites Work

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• A remark on the unique factorization theorem
• The \(D+XD_ s[X\) construction from GCD-domains]
• Prüfer v-multiplication domains and the ring \(R[X_{N_ v}\)]
• The class group of \(D+M\)
• Divisorial ideals and invertible ideals in a graded integral domain
• Splitting the t-class group
• On finite conductor domains
• The construction \(D+XD_s[X\)]
• \(t\)-splitting sets in integral domains.
• On the class group of a graded domain
• Almost splitting sets in integral domains
• Divisibility properties in semigroup rings
• On the class group and the local class group of a pullback
• Homogeneous splitting sets of a graded integral domain
• Some Results on v-Multiplication Rings

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