On divisorial ideals in polynomial rings over mori domains

DOI10.1080/00927878708823540zbMath0642.13017OpenAlexW2052200334MaRDI QIDQ3784240

Stefania Gabelli

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1080/00927878708823540

zbMATH Keywords

class groupKrull domainprime divisorial ideals of a polynomial ring over a Mori domain

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Ideals and multiplicative ideal theory in commutative rings (13A15) Divisibility and factorizations in commutative rings (13A05) Chain conditions, finiteness conditions in commutative ring theory (13E99)

Related Items (28)

The Class Group ofD[Γ forDan Integral Domain and Γ a Numerical Semigroup] ⋮ Star operations and primitive polynomials ⋮ GCD-Sets in Integral Domains. II ⋮ \(t\)-linked extensions, the \(t\)-class group, and Nagata's theorem ⋮ Numerical Semigroup Rings and Almost Prüferv-Multiplication Domains ⋮ Domains with the radical trace property and their complete integral closure ⋮ The class group of a strongly mori domain ⋮ Sur un theoreme de nagata ⋮ Almost splitting sets in integral domains. II ⋮ On t-invertibility II ⋮ Primary decomposition of divisorial ideals in Mori domains ⋮ Almost principal ideals in \(\mathrm R[x\)] ⋮ The class group of integral domains. ⋮ On locally AGCD domains ⋮ On \(t\)-dimension over strong Mori domains ⋮ UMT-domains: A Survey ⋮ A general theory of class groups ⋮ On Mori domains and commutative rings with \(CC^{\perp}\). II ⋮ Unique factorization and S-Picard groups of domains of power series ⋮ Splitting the t-class group ⋮ Two Extensions of a Star Operation on D to the Polynomial Ring D[X] ⋮ Almost splitting sets in integral domains ⋮ The local \(S\)-class group of an integral domain ⋮ Semigroup Rings as Weakly Factorial Domains ⋮ Unique factorization property of non-unique factorization domains ⋮ Mori domains of integer-valued polynomials ⋮ ALMOST SPLITTING SETS S OF AN INTEGRAL DOMAIN D SUCH THAT D_SIS A PID ⋮ On the class group of a graded domain

Cites Work

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• Idéaux divisoriels d'un anneau de polynômes
• Some remarks on star-operations
• Divisorial ideals and invertible ideals in a graded integral domain
• On a class of mori domains

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