Homogeneous splitting sets of a graded integral domain

DOI10.1016/j.jalgebra.2005.03.007zbMath1084.13001OpenAlexW1987412972MaRDI QIDQ2488317

Gyu Whan Chang, David F. Anderson

Publication date: 25 August 2005

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2005.03.007

zbMATH Keywords

Krull domainsplitting setgraded integral domaindecomposition of class group

Mathematics Subject Classification ID

Graded rings (13A02) Integral domains (13G05) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30) Class groups (13C20)

Related Items (23)

SEMIGROUP RINGS AS H-DOMAINS ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Semigroup rings as weakly Krull domains ⋮ Graded integral domains which are UMT-domains ⋮ Graded almost pseudo-valuation domains ⋮ UMT-domains: A Survey ⋮ Graded integral domains and Nagata rings ⋮ Graded integral domains in which each nonzero homogeneous t-ideal is divisorial ⋮ Semigroup rings as weakly factorial domains, II ⋮ Characterizations of graded Prüfer \(\star \)-multiplication domains. II ⋮ UMT-domain property in pullbacks of graded integral domains ⋮ Graded Prüfer domains ⋮ A characterization of weakly Krull monoid algebras ⋮ WHEN ARE GRADED INTEGRAL DOMAINS ALMOST GCD-DOMAINS ⋮ Discrete valuation overrings of a graded Noetherian domain ⋮ Weakly factorial property of a generalized Rees ring \(D[X,d/X\)] ⋮ Prüfer \(v\)-multiplication domains and related domains of the form \(D+D_S[\varGamma ^{*}\)] ⋮ The \(A + X B [X\) construction from Prüfer \(v\)-multiplication domains] ⋮ Graded Prüfer domains with Clifford homogeneous class semigroups ⋮ Semigroup Rings as Weakly Factorial Domains ⋮ Unique factorization property of non-unique factorization domains ⋮ Graded integral domains and Nagata rings, II

Cites Work

• On the converse of a well-known fact about Krull domains
• Prüfer v-multiplication domains and the ring \(R[X_{N_ v}\)]
• Divisorial ideals and invertible ideals in a graded integral domain
• Splitting the t-class group
• The class group of integral domains.
• \(t\)-splitting sets in integral domains.
• On the class group of a graded domain
• Divisibility properties in semigroup rings
• Weakly Krull and related domains of the form \(D+M, A+XB[X\) and \(A+X^2B[X]\)]
• Splitting sets in integral domains
• On t-invertibility II
• Weakly Factorial Domains and Groups of Divisibility
• Divisibility Properties of Graded Domains
• Graded krull domains
• The \(A+ XB[X\) and \(A+ XBX\) constructions from \(GCD\)-domains]
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