A Constructive Study About the Set of Intermediate Rings

DOI10.1080/00927872.2012.706842zbMath1288.13006OpenAlexW1993544729MaRDI QIDQ2863672

Ahmed Ayache

Publication date: 25 November 2013

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

Full work available at URL: https://doi.org/10.1080/00927872.2012.706842

zbMATH Keywords

boolean algebranormal pairnormal closureintegral extensionsfinite chain conditionorder isomorphism function

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Polynomials over commutative rings (13B25) Valuations and their generalizations for commutative rings (13A18) Extension theory of commutative rings (13B02) Other special types of modules and ideals in commutative rings (13C13)

Related Items

When is a fixed ring comparable to all overrings? ⋮ A special chain theorem in the set of intermediate rings ⋮ Unnamed Item ⋮ Boolean FIP ring extensions ⋮ Splitting ring extensions ⋮ WHEN IS THE INTEGRAL CLOSURE COMPARABLE TO ALL INTERMEDIATE RINGS ⋮ Quasi-Prüfer Extensions of Rings ⋮ On the commutative ring extensions with at most two non Prüfer intermediate rings ⋮ Pairs of domains where most of the intermediate domains are Prüfer ⋮ The Set of Intermediate Rings as a Boolean Algebra

Cites Work

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• Manis valuations and Prüfer extensions. I: A new chapter in commutative algebra
• On finiteness of chains of intermediate rings
• Intermediary rings in normal pairs
• Some finiteness chain conditions on the set of intermediate rings
• Couples d'anneaux partageant un idéal. (Couples of rings sharing an ideal)
• Divided rings and going-down
• Residually algebraic pairs of rings
• Homomorphismes minimaux d'anneaux
• ON THE LENGTHS OF MAXIMAL CHAINS OF INTERMEDIATE FIELDS IN A FIELD EXTENSION
• Ring extensions with some finiteness conditions on the set of intermediate rings
• A lower bound for the number of intermediary rings
• Some finiteness conditions on the set of overrings of an integral domain