Splitting the t-class group

DOI10.1016/0022-4049(91)90046-5zbMath0760.13006OpenAlexW2046369588MaRDI QIDQ1181495

David F. Anderson, Muhammad Zafrullah, Daniel D. Anderson

Publication date: 27 June 1992

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

Full work available at URL: https://doi.org/10.1016/0022-4049(91)90046-5

zbMATH Keywords

\(t\)-class group\(t\)-ideals

Mathematics Subject Classification ID

Class groups (13C20) Divisibility and factorizations in commutative rings (13A05)

Related Items (43)

ON INTEGRAL DOMAINS IN WHICH EVERY ASCENDING CHAIN ON PRINCIPAL IDEALS IS S-STATIONARY ⋮ The Class Group ofD[Γ forDan Integral Domain and Γ a Numerical Semigroup] ⋮ \(t\)-linked extensions, the \(t\)-class group, and Nagata's theorem ⋮ Various Facets of Rings BetweenD[X andK[X]] ⋮ On super v-domains ⋮ The class group of a strongly mori domain ⋮ Almost splitting sets in integral domains. II ⋮ Unnamed Item ⋮ Integral domains issued from associated primes ⋮ Arithmetic properties in pullbacks ⋮ Nagata-like theorems for almost Prüfer \(v\)-multiplication domains ⋮ A new characterization of GCD domains of formal power series ⋮ On the \(S\)-class group of the monoid algebra \(D[\Gamma\)] ⋮ The class group of integral domains. ⋮ Agreeable domains ⋮ Unnamed Item ⋮ A Schreier-type property for modules ⋮ Graded integral domains and Nagata rings ⋮ \(t\)-splitting sets in integral domains. ⋮ The \(D + E[\varGamma^*\) construction from Prüfer domains and GCD-domains] ⋮ On S-GCD domains ⋮ Unique factorization and S-Picard groups of domains of power series ⋮ Star operations and pullbacks. ⋮ Splitting sets in integral domains ⋮ A General Theory of Splitting Sets ⋮ WHEN ARE GRADED INTEGRAL DOMAINS ALMOST GCD-DOMAINS ⋮ Weakly factorial property of a generalized Rees ring \(D[X,d/X\)] ⋮ FACTORIZATION IN MONOID DOMAINS ⋮ Splitting multiplicative sets and elasticity ⋮ Long length functions ⋮ The \(A+ XB[X\) and \(A+ XBX\) constructions from \(GCD\)-domains] ⋮ Homogeneous splitting sets of a graded integral domain ⋮ Prüfer \(v\)-multiplication domains and related domains of the form \(D+D_S[\varGamma ^{*}\)] ⋮ t-splitting multiplicative sets of ideals in integral domains ⋮ Almost splitting sets in integral domains ⋮ LCM-splitting sets in some ring extensions ⋮ Almost Splitting Sets and AGCD Domains ⋮ A General Theory of Almost Splitting Sets ⋮ Factorization in integral domains. III ⋮ Mori domains of integer-valued polynomials ⋮ On the star class group of a pullback ⋮ Generalizations of Nagata’s theorem ⋮ t-SPLITTING SETS S OF AN INTEGRAL DOMAIN D SUCH THAT D_SIS A FACTORIAL DOMAIN

Cites Work

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• On Nagata's theorem for the class group
• Some remarks on star operations and the class group
• The \(D+XD_ s[X\) construction from GCD-domains]
• On primary factorizations
• Prüfer v-multiplication domains and the ring \(R[X_{N_ v}\)]
• The class group of \(D+M\)
• On Mori domains and commutative rings with \(CC^{\perp}\). I
• Factorization in integral domains. II
• On finite conductor domains
• Divisibility properties in semigroup rings
• On t-invertibility II
• Weakly Factorial Domains and Groups of Divisibility
• On t-invertibility
• On divisorial ideals in polynomial rings over mori domains
• A general theory of class groups
• Star-operations induced by overrings
• Convex Directed Subgroups of a Group of Divisibility

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