A CHARACTERIZATION OF THE COMMUTATIVE UNITAL RINGS WITH ONLY FINITELY MANY UNITAL SUBRINGS

DOI10.1142/S0219498808002990zbMath1173.13008OpenAlexW2061667480MaRDI QIDQ3602714

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

Publication date: 12 February 2009

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

Full work available at URL: https://doi.org/10.1142/s0219498808002990

zbMATH Keywords

ring extensionminimal ring extensionidealizationcrucial maximal idealFIP propertysingly generated ring

Mathematics Subject Classification ID

Integral domains (13G05) Integral dependence in commutative rings; going up, going down (13B21) Rings of fractions and localization for commutative rings (13B30) Commutative ring extensions and related topics (13B99) Finite commutative rings (13M99)

Related Items (5)

Unital rings with cardinality restrictions on unital subrings ⋮ Characterizing the ring extensions that satisfy FIP or FCP ⋮ Δ-Extension of rings and invariance properties of ring extension under group action ⋮ On λ-extensions of commutative rings ⋮ Commutative rings with infinitely many maximal subrings

Cites Work

• Unnamed Item
• A classification of the minimal ring extensions of an integral domain
• Homomorphismes minimaux d'anneaux
• The Singly Generated Unital Rings with Only Finitely Many Unital Subrings
• On the FIP Property for Extensions of Commutative Rings

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