Kronecker Function Rings and Generalized Integral Closures

DOI10.1081/AGB-120016775zbMath1073.13507OpenAlexW2017382943MaRDI QIDQ4803370

Franz Halter-Koch

Publication date: 2 April 2003

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

Full work available at URL: https://doi.org/10.1081/agb-120016775

zbMATH Keywords

star operationalgebraic field extensionsideal systemKronecker function rings

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Integral closure of commutative rings and ideals (13B22) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Integral domains (13G05) Ideals and multiplicative ideal theory in commutative rings (13A15)

Related Items (20)

Local–Global Properties for Semistar Operations ⋮ Semistar Dedekind domains ⋮ Kronecker Function Rings of Transcendental Field Extensions ⋮ The Zariski-Riemann Space of Valuation Rings ⋮ Topological properties of semigroup primes of a commutative ring ⋮ Some Closure Operations in Zariski-Riemann Spaces of Valuation Domains: A Survey ⋮ Open Problems in Commutative Ring Theory ⋮ Projective star operations on polynomial rings over a field ⋮ Kronecker function rings of ring extensions ⋮ Affine schemes and topological closures in the Zariski-Riemann space of valuation rings ⋮ Localizing systems, module systems, and semistar operations ⋮ \(\ast\)-Noetherian domains and the ring \(D[x_N\)] ⋮ Some applications of the ultrafilter topology on spaces of valuation domains, Part II ⋮ A generalization of Kronecker function rings and Nagata rings ⋮ The upper Vietoris topology on the space of inverse-closed subsets of a spectral space and applications ⋮ An Overring-Theoretic Approach to Polynomial Extensions of Star and Semistar Operations ⋮ Topological Aspects of Irredundant Intersections of Ideals and Valuation Rings ⋮ The space of homogeneous preserving semistar operations on graded domains ⋮ Lorenzen Monoids: A Multiplicative Approach to Kronecker Function Rings ⋮ The constructible topology on spaces of valuation domains

Cites Work

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• Rings with a theory of greatest common divisors
• Beiträge zur Arithmetik kommutativer Integritätsbereiche. I: Multiplikationsringe, ausgezeichnete Idealsysteme und Kroneckersche Funktionalringe
• Beiträge zur Arithmetik kommutativer Integritätsbereiche. II. \(v\)- Ideale und vollständig ganz abgeschlossene Integritätsbereiche

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