Intermediary rings in normal pairs

DOI10.1016/j.jpaa.2008.03.002zbMath1148.13003OpenAlexW2074572339MaRDI QIDQ932287

Noômen Jarboui, Ahmed Ayache

Publication date: 10 July 2008

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

Full work available at URL: https://doi.org/10.1016/j.jpaa.2008.03.002

zbMATH Keywords

Prüfer domainintermediate ringsNoetherian domainoverringintegral closureprime spectrummaximal spectrumheight of an idealKaplansky transform of a ring with respect to an idealnormal pair of ringsSupp(S/R)totally ordered set of rings

Mathematics Subject Classification ID

Commutative Noetherian rings and modules (13E05) Polynomials over commutative rings (13B25) Valuations and their generalizations for commutative rings (13A18) Extension theory of commutative rings (13B02) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15)

Related Items (15)

Unnamed Item ⋮ Splitting ring extensions ⋮ Characterizing the ring extensions that satisfy FIP or FCP ⋮ WHEN IS THE INTEGRAL CLOSURE COMPARABLE TO ALL INTERMEDIATE RINGS ⋮ Δ-Extension of rings and invariance properties of ring extension under group action ⋮ FROM TOPOLOGIES OF A SET TO SUBRINGS OF ITS POWER SET ⋮ An algorithm for computing the number of intermediary rings in normal pairs ⋮ On λ-extensions of commutative rings ⋮ The set of indeterminate rings of a normal pair as a partially ordered set ⋮ Some finiteness chain conditions on the set of intermediate rings ⋮ THE FERRAND-OLIVIER CLASSIFICATION OF THE MINIMAL RING EXTENSIONS OF A FIELD: A PROOF AND A SURVEY OF ITS INFLUENCE ⋮ Finite maximal chains of commutative rings ⋮ Transfer Results for the FIP and FCP Properties of Ring Extensions ⋮ On questions related to normal pairs ⋮ A Constructive Study About the Set of Intermediate Rings

Cites Work

• The S-transform and the ideal transform
• Residually algebraic pairs of rings
• Maximal non-Noetherian subrings of a domain.
• Pairs of domains where all intermediate domains are Jaffard
• Overrings of Commutative Rings. III: Normal Pairs
• A lower bound for the number of intermediary rings
• Some finiteness conditions on the set of overrings of an integral domain
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