When is \(C(X)/P\) a valuation ring for every prime ideal \(P\)?

DOI10.1016/0166-8641(92)90091-DzbMath0801.54014OpenAlexW2088130720MaRDI QIDQ1203833

Richard G. Wilson, Melvin Henriksen

Publication date: 18 February 1993

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0166-8641(92)90091-d

zbMATH Keywords

valuation ringStone-Čech compactificationminimal prime ideal\(F\)-spacering of continuous real-valued functionsTikhonov space\(C^*\)-embedded SV-spacesreal-closed ring

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Algebraic properties of function spaces in general topology (54C40) Ordered rings, algebras, modules (06F25)

Related Items (18)

Quasi SV-frames and their properties ⋮ A closer look at primal and pseudo-irreducible ideals with applications to rings of functions ⋮ Constructing Rings of Continuous Functions in Which There Are Many Maximal Ideals with Nontrivial Rank ⋮ Variations of essentiality of ideals in commutative rings ⋮ Rings of Continuous Functions on Spaces of Finite Rank and the SV Property ⋮ Pseudo-valuation rings and \(C(X)\) ⋮ l-Ideals of the form , ideals satisfying , and primary mdeals in a class of f-rings ⋮ Unnamed Item ⋮ Some set-theory, Stone-Čech, and \(F\)-spaces ⋮ Finitely 1-convex \(f\)-rings ⋮ SV and related \(f\)-rings and spaces ⋮ SV-rings and SV-porings ⋮ Concerning real-closed ideals in \(\mathcal{R} L\) and SV-frames ⋮ f-rings in which every maximal ideal contains finitely many minimal prime ideals ⋮ Lattice-Ordered Algebras that are Subdirect Products of Valuation Domains ⋮ Images and Open Subspaces of SV Spaces ⋮ Conditions on Normal Spaces of Finite Rank That GuaranteeC(X) is SV ⋮ A note on spaces that are finitely an \(F\)-space.

Cites Work

• Unnamed Item
• Almost discrete SV-space
• Ideals in rings of continuous functions
• Real closed rings, I. Residue rings of rings of continuous functions
• The Space of Minimal Prime Ideals of a Commutative Ring

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