Prime and maximal ideals in subrings of C(X)

DOI10.1016/0166-8641(91)90057-SzbMath0732.54016MaRDI QIDQ808465

H. Linda Byun, Saleem Watson

Publication date: 1991

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

zbMATH Keywords

maximal idealsprime idealz-filterz-ideal

Mathematics Subject Classification ID

Algebraic properties of function spaces in general topology (54C40) Rings and algebras of continuous, differentiable or analytic functions (46E25)

Related Items (19)

Intermediate algebras between \(C^*(X)\) and \(C(X)\) as rings of fractions of \(C^*(X)\) ⋮ Local invertibility in subrings of C*(X) ⋮ Unnamed Item ⋮ Rings and sheaves ⋮ A correspondence between ideals and \(z\)-filters for certain rings of continuous functions -- some remarks ⋮ Notes on a class of ideals in intermediate rings of continuous functions ⋮ C(X) determines X - a unified theory ⋮ On the sum of \(z\)-ideals in subrings of \(C(X)\) ⋮ Characterizations of ideals in intermediate \(C\)-rings \(A(X)\) via the \(A\)-compactifications of \(X\) ⋮ On the mappings ${\mathcal Z}_A$ and $\Im_A$ in intermediate rings of $C(X)$ ⋮ On the cardinality of non-isomorphic intermediate rings of \(C(X)\) ⋮ Rings and subrings of continuous functions with countable range ⋮ Abundance of isomorphic and non isomorphic \(C\)-type intermediate rings ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Intermediate rings of complex-valued continuous functions ⋮ Unnamed Item ⋮ A note on ideals of \(C_\infty(X)\) ⋮ \(A\)-compactness and minimal subalgebras of \(C(X)\)

Cites Work

• Unnamed Item
• Groupes et anneaux reticules
• Stone-Čech compactification of a product
• Rings with Hausdorff structure space
• Ideals in rings of continuous functions
• On the structure of a class of archimedean lattice-ordered algebras
• Residue class fields of lattice-ordered algebras
• Maximal Ideals in Subalgebras of C(X)
• On a class of subalgebras of C(X) with applications to βX\X
• Supports of Continuous Functions
• A ring of analytic functions
• Topological Rings
• Concerning Rings of Continuous Functions

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