A general theory of class groups

DOI10.1080/00927878808823604zbMath0648.13002OpenAlexW2015817329MaRDI QIDQ3792775

David F. Anderson

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1080/00927878808823604

zbMATH Keywords

class groupstar operationfractional ideal

Mathematics Subject Classification ID

Ideals and multiplicative ideal theory in commutative rings (13A15) Divisibility and factorizations in commutative rings (13A05) Theory of modules and ideals in commutative rings (13C99)

Related Items (30)

Star operations and primitive polynomials ⋮ \(t\)-linked extensions, the \(t\)-class group, and Nagata's theorem ⋮ The class group of a strongly mori domain ⋮ ∗-Almost super-homogeneous ideals in ∗-h-local domains ⋮ Star operations and pullbacks. ⋮ THE v-OPERATION IN EXTENSIONS OF INTEGRAL DOMAINS ⋮ Almost Bézout domains ⋮ Splitting the t-class group ⋮ On semi-Krull domains ⋮ Semistar Invertibility on Integral Domains ⋮ Functorial Properties of Star Operations ⋮ Some remarks on Prüfer \(\bigstar\)-multiplication domains and class groups ⋮ A General Theory of Splitting Sets ⋮ Elasticity of factorizations in integral domains ⋮ A note on *_{𝑤}-Noetherian domains ⋮ On Local ☆-Completely Integrally Closed Domains ⋮ Star operations and the \(D + M\) construction ⋮ Splitting multiplicative sets and elasticity ⋮ Jaffard families and localizations of star operations ⋮ The \(A+ XB[X\) and \(A+ XBX\) constructions from \(GCD\)-domains] ⋮ Star operations in extensions of integral domains ⋮ On Nagata's theorem for the class group ⋮ Onv-Domains and Star Operations ⋮ Clifford semigroups of ideals in monoids and domains ⋮ Star Almost Schreier Domains ⋮ A General Theory of Almost Splitting Sets ⋮ Mori domains of integer-valued polynomials ⋮ On the star class group of a pullback ⋮ On the class group of a pullback ⋮ Stability and Clifford Regularity with Respect to Star Operations

Cites Work

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• A general theory of almost factoriality
• On \(\text{Pic}(R[X)\) for \(R\) seminormal]
• Idéaux divisoriels d'un anneau de polynômes
• Some remarks on star-operations
• On Pruefer v-multiplication domains
• \(D+M\) constructions with general overrings
• On finite conductor domains
• The construction \(D+XD_s[X\)]
• Overrings and divisorial ideals of rings of the form \(D+M\)
• Characterizations of ^*-Multiplication Domains
• On divisorial ideals in polynomial rings over mori domains
• The Local Class Group of a Krull Domain
• Some Results on v-Multiplication Rings

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