Transfer Results for the FIP and FCP Properties of Ring Extensions

DOI10.1080/00927872.2013.856440zbMath1317.13016OpenAlexW2089811611MaRDI QIDQ5249921

David E. Dobbs, Gabriel Picavet, Martine Picavet-L'Hermitte

Publication date: 13 May 2015

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

Full work available at URL: https://doi.org/10.1080/00927872.2013.856440

zbMATH Keywords

seminormalizationring extensionNagata ringschain of subalgebras

Mathematics Subject Classification ID

Polynomials over commutative rings (13B25) Extension theory of commutative rings (13B02) Integral dependence in commutative rings; going up, going down (13B21)

Related Items (18)

Maximal non-prime ideally equal subrings of a commutative ring ⋮ Pointwise minimal extensions ⋮ Catenarian FCP ring extensions ⋮ The Loewy series of an FCP (distributive) ring extension ⋮ A special chain theorem in the set of intermediate rings ⋮ Boolean FIP ring extensions ⋮ Splitting ring extensions ⋮ Around Prüfer Extensions of Rings ⋮ Unnamed Item ⋮ On strongly affine extensions of commutative rings ⋮ Quasi-Prüfer Extensions of Rings ⋮ Étale extensions with finitely many subextensions ⋮ FCP \(\Delta\)-extensions of rings ⋮ Residually FCP extensions of commutative rings ⋮ THE FERRAND-OLIVIER CLASSIFICATION OF THE MINIMAL RING EXTENSIONS OF A FIELD: A PROOF AND A SURVEY OF ITS INFLUENCE ⋮ Ring extensions of length two ⋮ When an extension of Nagata rings has only finitely many intermediate rings, each of those is a Nagata ring ⋮ A note on the FIP property for extensions of commutative rings

Cites Work

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• Characterizing minimal ring extensions
• Intermediary rings in normal pairs
• Characterizing the ring extensions that satisfy FIP or FCP
• Homomorphismes minimaux d'anneaux
• ON THE LENGTHS OF MAXIMAL CHAINS OF INTERMEDIATE FIELDS IN A FIELD EXTENSION
• The Singly Generated Unital Rings with Only Finitely Many Unital Subrings
• Proprietes et applications de la notion de contenu
• Morphismes t- clos
• A lower bound for the number of intermediary rings
• On the FIP Property for Extensions of Commutative Rings
• On seminormality

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