Rings of continuous functions with values in a topological division ring

DOI10.1007/BF02363066zbMath0868.46018OpenAlexW2077321328MaRDI QIDQ1918663

E. M. Vechtomov

Publication date: 30 October 1996

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02363066

zbMATH Keywords

dualitiesrings of continuous functionsdivisibilityleast common multiplesgreatest common divisorsGelfand-Kolmogorov theoremdecomposable idealsBézout-ringGelfand subringKaplansky problemprime and semiprime idealspure and projective idealsvalues in a topological division ring

Mathematics Subject Classification ID

Function spaces in general topology (54C35) Algebraic properties of function spaces in general topology (54C40) Rings and algebras of continuous, differentiable or analytic functions (46E25)

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Cites Work

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• Unnamed Item
• Compact ringed spaces
• Zero-dimensional spaces
• Convex and pseudoprime ideals in rings of continuous functions
• Projectivity of pure ideals
• Self-injective simple Pierce sheaves
• Module of all functions over the ring of continuous functions
• A generalisation of Gel'fand duality
• Noncommutative rings in which every prime ideal is contained in a unique maximal ideal
• Continuous selections and stable rank of Banach algebras
• An application of compactifications: Some theorems of maximal ideals
• Projective ideals in rings of continuous functions
• The Stone-Weierstrass theorem for valuable fields
• Non-Archimedean Gelfand theory
• Further results on E-compact spaces. I
• On two sum theorems for ideals of \(C(X)\)
• On a representation of a strongly harmonic ring by sheaves
• Paracompactness of locally compact Hausdorff spaces
• Rings of continuous functions with values in a non-archimedean ordered field
• Rings of continuous functions with values in an Archimedean ordered field
• Topological methods in valuation theory
• Maximal ideals in rings of bounded continuous functions
• On the Gel'fand-Kolmogorov theorem on maximal ideals of rings of continuous functions
• On Rings of Bounded Continuous Functions with Values in a Division Ring
• Rings of Continuous Functions in Which Every Finitely Generated Ideal is Principal
• Rings with Hausdorff structure space
• Characters of Cartesian Products of Algebras
• Direct Products of Modules
• A Sheaf Representation for Modules with Applications to Gelfand Rings
• Sheaf representations of strongly harmonic rings
• Ideal Theory in f-Algebras
• Rings of Continuous Functions with Values in a Topological Field
• On Projective Prime Ideals in C(X)
• Strongly semiprime modules and rings
• Rings of continuous functions and sheaves of rings
• Modules over commutative regular rings
• Commutative Rings in Which Every Prime Ideal is Contained in a Unique Maximal Ideal
• Uniqueness of Generators of Principal Ideals in Rings of Continuous Functions
• On the Representation of Modules by Sheaves of Factor Modules
• Structures of continuous functions. I
• Representations of algebras by continuous sections
• Applications of the Theory of Boolean Rings to General Topology
• Rings of Real-Valued Continuous Functions. I
• Topological Rings
• On a Theorem of Gelfand and Kolmogoroff Concerning Maximal Ideals in Rings of Continuous Functions
• Concerning Rings of Continuous Functions
• Über nulldimensionale Räume

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