Ring extensions of length two

DOI10.1142/S0219498819501743zbMath1423.13059arXiv1803.11297OpenAlexW2888942678MaRDI QIDQ5231721

Martine Picavet-L'Hermitte, Gabriel Picavet

Publication date: 27 August 2019

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.11297

zbMATH Keywords

minimal extensionseparable field extensionintegral extensionFCP extensionFIPsupport of a modulealgebraic field extensionpointwise minimal extension\(t\)-closurelength of an extensionprincipal subfield

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Morphisms of commutative rings (13B10) Integral domains (13G05) Extension theory of commutative rings (13B02) Integral dependence in commutative rings; going up, going down (13B21) Rings of fractions and localization for commutative rings (13B30)

Related Items (8)

An answer to a question about maximal non-integrally closed subrings ⋮ Catenarian FCP ring extensions ⋮ The Loewy series of an FCP (distributive) ring extension ⋮ Unnamed Item ⋮ Boolean FIP ring extensions ⋮ Splitting ring extensions ⋮ Unnamed Item ⋮ FCP \(\Delta\)-extensions of rings

Cites Work

• Manis valuations and Prüfer extensions. I: A new chapter in commutative algebra
• Pointwise minimal extensions
• The complexity of computing all subfields of an algebraic number field
• Generating subfields
• Characterizing the ring extensions that satisfy FIP or FCP
• When an extension of Nagata rings has only finitely many intermediate rings, each of those is a Nagata ring
• Homomorphismes minimaux d'anneaux
• Morphismes t- clos
• Quasi-Prüfer Extensions of Rings
• Prüfer and Morita Hulls of FCP Extensions
• Transfer Results for the FIP and FCP Properties of Ring Extensions
• VALUATIVE DOMAINS
• On the existence of exceptional field extensions
• On seminormality
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