The class group of integral domains.

DOI10.1016/S0021-8693(03)00139-XzbMath1053.13003MaRDI QIDQ1399183

Gyu Whan Chang, David F. Anderson

Publication date: 30 July 2003

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

zbMATH Keywords

class grouppullbackMori domainPVMDNagata theorem

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) Class groups (13C20)

Related Items (8)

\(t\)-splitting sets in integral domains. ⋮ Unique factorization and S-Picard groups of domains of power series ⋮ A General Theory of Splitting Sets ⋮ Unnamed Item ⋮ Homogeneous splitting sets of a graded integral domain ⋮ Almost splitting sets in integral domains ⋮ The Class Group of Pullbacks ⋮ On the star class group of a pullback

Cites Work

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• On Nagata's theorem for the class group
• The rings R(X) and \(R<X>\)
• Some remarks on star operations and the class group
• Prüfer v-multiplication domains and the ring \(R[X_{N_ v}\)]
• The class group of \(D+M\)
• Integral domains in which each t-ideal is divisorial
• On \(\text{Pic}(R[X)\) for \(R\) seminormal]
• Splitting the t-class group
• Factorization in integral domains. II
• Flat ideals. II
• On finite conductor domains
• The construction \(D+XD_s[X\)]
• On the class group and the local class group of a pullback
• \(t\)-linked extensions, the \(t\)-class group, and Nagata's theorem
• On t-invertibility II
• On divisorial ideals in polynomial rings over mori domains
• Some Results on v-Multiplication Rings

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