On the sum of \(z\)-ideals in subrings of \(C(X)\)

DOI10.1216/jca.2020.12.459zbMath1460.54012OpenAlexW3118891897MaRDI QIDQ2219237

Mehdi Parsinia, F. Azarpanah

Publication date: 19 January 2021

Published in: Journal of Commutative Algebra (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jca/1609815620

zbMATH Keywords

\(z\)-idealintermediate algebra\(z_A\)-idealabsolutely convex subringintermediate subalgebra of \(C(X)\)

Mathematics Subject Classification ID

Banach algebras of continuous functions, function algebras (46J10) Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) Algebraic properties of function spaces in general topology (54C40) Real-valued functions in general topology (54C30) Rings and algebras of continuous, differentiable or analytic functions (46E25)

Related Items (7)

Constructing the Banaschewski compactification through the functionally countable subalgebra of $C(X)$ ⋮ Notes on a class of ideals in intermediate rings of continuous functions ⋮ Remarks on intermediate C-rings of C(X) ⋮ Rings and subrings of continuous functions with countable range ⋮ Unnamed Item ⋮ On the sum of \(z^\circ\)-ideals in two classes of subrings of \(C(X)\) ⋮ R-P-spaces and subrings of C(X)

Cites Work

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• Intermediate algebras between \(C^*(X)\) and \(C(X)\) as rings of fractions of \(C^*(X)\)
• On subrings of the form \(I+\mathbb{R}\) of \(C(X)\)
• On two sum theorems for ideals of \(C(X)\)
• Sums of Semiprime, z, and d l-Ideals in a Class of f-Rings
• Prime z-Ideals of C(X) and Related Rings
• On Structure Spaces of Ideals In Rings of Continuous Functions
• On a class of subalgebras of C(X) with applications to βX\X
• Remarks on $LBI$-subalgebras of $C(X)$

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