On Nagata's theorem for the class group

DOI10.1016/0022-4049(90)90122-XzbMath0717.13010MaRDI QIDQ753871

Moshe Roitman, Stefania Gabelli

Publication date: 1990

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

zbMATH Keywords

class groupsKrull domainsMori domainarchimedean domainNagata's theorem

Mathematics Subject Classification ID

Ideals and multiplicative ideal theory in commutative rings (13A15) Commutative rings and modules of finite generation or presentation; number of generators (13E15) Class groups (13C20)

Related Items (16)

\(t\)-linked extensions, the \(t\)-class group, and Nagata's theorem ⋮ One-dimensional stable rings ⋮ The class group of a strongly mori domain ⋮ Ten Problems on Stability of Domains ⋮ Open Problems in Commutative Ring Theory ⋮ The class group of integral domains. ⋮ Splitting sets in integral domains ⋮ Splitting the t-class group ⋮ On finitely stable domains. I ⋮ Factorization in integral domains. II ⋮ Reduced Archimedean skew polynomial rings and skew power series rings ⋮ Unnamed Item ⋮ Characterizations of *-Cancellation Ideals of an Integral Domain ⋮ Mori domains of integer-valued polynomials ⋮ On the star class group of a pullback ⋮ Generalizations of Nagata’s theorem

Cites Work

• How far is a Mori domain from being a Krull domain ?
• On the class group of a Mori domain
• Some remarks on star operations and the class group
• The \(D+XD_ s[X\) construction from GCD-domains]
• The class group of \(D+M\)
• A general theory of class groups
• The Local Class Group of a Krull Domain
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On Nagata's theorem for the class group