On maximal ideals of \(C_c(X)\) and the uniformity of its localizations

DOI10.1216/RMJ-2018-48-2-345zbMath1395.54013OpenAlexW2807569996MaRDI QIDQ1638039

A. R. Olfati, F. Azarpanah, Z. Keshtkar, Omid Ali Shahny Karamzadeh

Publication date: 12 June 2018

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1528077621

zbMATH Keywords

cleanzero-dimensional\(F\)-spaceBézout ring\(z_c\)-ideal\(F_c\)-space

Mathematics Subject Classification ID

Algebraic properties of function spaces in general topology (54C40)

Related Items (20)

Ordered field valued continuous functions with countable range ⋮ On CP-frames ⋮ Intrinsic characterizations of C-realcompact spaces ⋮ Closed ideals in the functionally countable subalgebra of C(X) ⋮ On some properties of the space of minimal prime ideals of 𝐶𝑐 (𝑋) ⋮ Constructing the Banaschewski compactification through the functionally countable subalgebra of $C(X)$ ⋮ Intermediate rings of a class of ordered field valued continuous functions ⋮ Almost clean elements in C(X) ⋮ Unnamed Item ⋮ p-semisimple modules and type submodules ⋮ Self-injectivity of M(X,A) versus M(X,A) modulo its socle ⋮ Locally functionally countable subalgebra of $\mathcal{R}(L)$ ⋮ Unnamed Item ⋮ Rings with only finitely many essential right ideals ⋮ \(C(X)\) versus its functionally countable subalgebra ⋮ On c-realcompact spaces ⋮ Unnamed Item ⋮ Rings and subrings of continuous functions with countable range ⋮ On countably uniform closed-spaces ⋮ Further thoughts on the ring \(\mathcal{R}_c(L)\) in frames

Cites Work

• On the functionally countable subalgebra of \(C(X)\)
• When is \(C(X)\) a clean ring?
• \(C(X)\) versus its functionally countable subalgebra
• Idempotent generated algebras and Boolean powers of commutative rings
• Rings of continuous functions with values in an Archimedean ordered field
• The classical ring of quotients of $C_c(X)$
• Goldie dimension of rings of fractions ofC(X)
• On the locally functionally countable subalgebra of C(X) on locally functionally countable subalgebra of C(X)
• Clean Semiprimef-Rings with Bounded Inversion
• Study of Hopficity in Certain Classes of Rings
• On Inverse-Closed Subalgebras of C (X )^†
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