The \(A+ XB[X]\) and \(A+ XB[[X]]\) constructions from \(GCD\)-domains

DOI10.1016/S0022-4049(00)00066-9zbMath1004.13004MaRDI QIDQ5935969

Driss Nour El Abidine, David F. Anderson

Publication date: 16 February 2003

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

zbMATH Keywords

extension of integral domainsGCD-domainPrüfer \(v\)-multiplication

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Integral domains (13G05) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Formal power series rings (13F25)

Related Items (13)

Ascending Nets of Prüfer V-Multiplication Domains ⋮ Various Facets of Rings BetweenD[X andK[X]] ⋮ Module-Theoretic Characterizations of Generalized GCD Domains ⋮ Valuation ideals and primary \(w\)-ideals ⋮ Arithmetic properties in pullbacks ⋮ A new characterization of GCD domains of formal power series ⋮ Ring-theoretic properties of commutative algebras of invariants. ⋮ When is \(A+XBX\) Noetherian? ⋮ Homogeneous splitting sets of a graded integral domain ⋮ The Class Group of Pullbacks ⋮ The \(A + X B [X\) construction from Prüfer \(v\)-multiplication domains] ⋮ Nearly Krull domains and nearly Prüfer \(v\)-multiplication domains ⋮ Unique factorization property of non-unique factorization domains

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Well behaved prime t-ideals
• The \(D+XD_ s[X\) construction from GCD-domains]
• Couples d'anneaux partageant un idéal. (Couples of rings sharing an ideal)
• The class group of \(D+M\)
• On Pruefer v-multiplication domains
• Splitting the t-class group
• \(D+M\) constructions with general overrings
• The construction \(D+XD_s[X\)]
• Factorization in integral domains. III
• Associated primes of principal idelals
• On the class group and the local class group of a pullback
• Overrings and divisorial ideals of rings of the form \(D+M\)
• A general theory of class groups
• The Local Class Group of a Krull Domain
• The class group of a strongly mori domain
• Some Results on v-Multiplication Rings

This page was built for publication: The \(A+ XB[X]\) and \(A+ XBX\) constructions from \(GCD\)-domains