Minimal Overrings of an Integrally Closed Domain

DOI10.1081/AGB-120024849zbMath1029.13004OpenAlexW2043941510MaRDI QIDQ4435153

Ahmed Ayache

Publication date: 26 November 2003

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

Full work available at URL: https://doi.org/10.1081/agb-120024849

zbMATH Keywords

spectrumDedekind domainKrull domainintegrally closed domainideal transformsminimal overring of polynomial ringminimal overringsPrüferian domain

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Integral domains (13G05) Extension theory of commutative rings (13B02) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (19)

Conch maximal subrings ⋮ On Finite Saturated Chains of Overrings ⋮ Strongly divided domains ⋮ VALUATIVE DOMAINS ⋮ A classification of the minimal ring extensions of an integral domain ⋮ A classification of the minimal ring extensions of certain commutative rings ⋮ Maximal subrings of classical integral domains ⋮ When the Semistar Operation is the Identity ⋮ Δ-Extension of rings and invariance properties of ring extension under group action ⋮ On λ-extensions of commutative rings ⋮ The set of indeterminate rings of a normal pair as a partially ordered set ⋮ A corrigendum to ``Hereditary properties between a ring and its maximal subrings ⋮ Pointwise maximal subrings ⋮ THE FERRAND-OLIVIER CLASSIFICATION OF THE MINIMAL RING EXTENSIONS OF A FIELD: A PROOF AND A SURVEY OF ITS INFLUENCE ⋮ On Minimal Extensions of Rings ⋮ Finite maximal chains of commutative rings ⋮ Every Commutative Ring Has a Minimal Ring Extension ⋮ The Set of Intermediate Rings as a Boolean Algebra ⋮ FINITELY VALUATIVE DOMAINS

Cites Work

• Unnamed Item
• The S-transform and the ideal transform
• Residually algebraic pairs of rings
• The ideal transform and overrings of an integral domain
• On flat overrings, ideal transforms and generalized transforms of a commutative ring
• The Dimension Sequence of a Commutative Ring
• Local Minimal Overrings
• Integral domains whose overrings are ideal transforms

This page was built for publication: Minimal Overrings of an Integrally Closed Domain