Some finiteness conditions on the set of overrings of an integral domain

DOI10.1090/S0002-9939-02-06816-8zbMath1017.13009MaRDI QIDQ4804087

Robert Gilmer

Publication date: 10 April 2003

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Prüfer domainintegral domainfinite prime spectrumfinite chains of overrings

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Integral domains (13G05) Commutative rings and modules of finite generation or presentation; number of generators (13E15) Extension theory of commutative rings (13B02) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (46)

A FINITENESS CONDITION ON QUASI-LOCAL OVERRINGS OF A CLASS OF PINCHED DOMAINS ⋮ Conch maximal subrings ⋮ On finiteness of chains of intermediate rings ⋮ When is a fixed ring comparable to all overrings? ⋮ A question about maximal non-valuation subrings ⋮ Isonoetherian power series rings ⋮ A special chain theorem in the set of intermediate rings ⋮ Maximal non-integrally closed subrings of an integral domain ⋮ Counting intermediate rings in normal pairs ⋮ Graph theoretic characterizations of maximal non-valuation subrings of a field ⋮ Characterizing the ring extensions that satisfy FIP or FCP ⋮ Numerical characterizations of some integral domains ⋮ The number of intermediate rings in FIP extension of integral domains ⋮ WHEN IS THE INTEGRAL CLOSURE COMPARABLE TO ALL INTERMEDIATE RINGS ⋮ Δ-Extension of rings and invariance properties of ring extension under group action ⋮ Maximal non valuation domains in an integral domain ⋮ Intermediary rings in normal pairs ⋮ On strongly affine extensions of commutative rings ⋮ Maximal non $\lambda$-subrings ⋮ An algorithm for computing the number of intermediary rings in normal pairs ⋮ Note on the divisoriality of domains of the form $k[[X^{p}, X^{q}]$, $k[X^{p}, X^{q}]$, $k[[X^{p}, X^{q}, X^{r}]]$, and $k[X^{p}, X^{q}, X^{r}]$] ⋮ On the FIP Property for Extensions of Commutative Rings ⋮ On λ-extensions of commutative rings ⋮ Characterizations of Some Classes of Integral Domains via Semistar Operations ⋮ Étale extensions with finitely many subextensions ⋮ MAXIMAL NON-PRÜFER AND MAXIMAL NON-INTEGRALLY CLOSED SUBRINGS OF A FIELD ⋮ The set of indeterminate rings of a normal pair as a partially ordered set ⋮ A Note on Going Down Domains ⋮ Some finiteness chain conditions on the set of intermediate rings ⋮ Residually FCP extensions of commutative rings ⋮ On the set of \(t\)-linked overrings of an integral domain ⋮ An answer to a problem about the number of overrings ⋮ Ring extensions with some finiteness conditions on the set of intermediate rings ⋮ Extensions of Integral Domains with Infinite Chains of Intermediate Rings ⋮ Krull dimension, overrings and semistar operations of an integral domain ⋮ THE FERRAND-OLIVIER CLASSIFICATION OF THE MINIMAL RING EXTENSIONS OF A FIELD: A PROOF AND A SURVEY OF ITS INFLUENCE ⋮ On the existence of maximal subrings in commutative noetherian rings ⋮ Finite maximal chains of commutative rings ⋮ The Space of Maximal Subrings of a Commutative Ring ⋮ Isonoetherian power series rings II ⋮ A finiteness condition on the set of overrings of some classes of integral domains ⋮ A Constructive Study About the Set of Intermediate Rings ⋮ A note on the FIP property for extensions of commutative rings ⋮ A Zariski topology on integrally closed maximal subrings of a commutative ring ⋮ Commutative rings with infinitely many maximal subrings ⋮ The number of overrings of an integrally closed domain

Cites Work

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• Finitely generated intermediate rings
• A characterization of Prüfer domains in terms of polynomials
• Residually algebraic pairs of rings
• The pseudo-radical of a commutative ring
• The converse to a well known theorem on Noetherian rings
• Intersections of quotient rings of an integral domain
• Hilbert rings and the Hilbert Nullstellensatz
• A lower bound for the number of intermediary rings

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