Arithmetic properties in pullbacks

DOI10.1016/j.jalgebra.2007.01.007zbMath1117.13024OpenAlexW1997418846MaRDI QIDQ876349

John Taylor, Evan G. jun. Houston

Publication date: 18 April 2007

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2007.01.007

zbMATH Keywords

GCD-domain, Prüfer, pullback, PVMD, star operation, \(t\)-ideal, \(t\)-linked \(v\)-domain, \(v\)-ideal, \(v\)-linked

Mathematics Subject Classification ID

Integral domains (13G05) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items

Maximal non-prime ideally equal subrings of a commutative ring ⋮ Module-Theoretic Characterizations of Generalized GCD Domains ⋮ Directed unions of local monoidal transforms and GCD domains ⋮ Divisorial Prime Ideals in Prüfer Domains ⋮ Bhargava rings that are Prüfer v-multiplication domains ⋮ Functorial Properties of Star Operations ⋮ On the commutative ring extensions with at most two non Prüfer intermediate rings ⋮ Some remarks on Prüfer rings with zero-divisors ⋮ Divisorial behavior of prime ideals in Prüfer domains ⋮ Uppers to Zero in Polynomial Rings and Prüfer-Like Domains ⋮ Prüfer conditions in amalgamated algebras ⋮ The Kaplansky condition and rings of almost stable range 1 ⋮ Pairs of domains where most of the intermediate domains are Prüfer

Cites Work

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• On divisorial prime ideals in Prüfer v-multiplication domains
• The \(D+XD_ s[X\) construction from GCD-domains]
• Prüfer v-multiplication domains and the ring \(R[X_{N_ v}\)]
• Couples d'anneaux partageant un idéal. (Couples of rings sharing an ideal)
• Topologically defined classes of commutative rings
• Splitting the t-class group
• The construction \(D+XD_s[X\)]
• On the class group of a pullback
• On the class group and the local class group of a pullback
• t-Linked overrings and prüfer v-multiplication domains
• Intersections of Quasi-Local Domains
• Some Results on v-Multiplication Rings
• An Essential Ring Which is Not A v-Multiplication Ring
• The \(A+ XB[X\) and \(A+ XBX\) constructions from \(GCD\)-domains]

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