Rings and sheaves

DOI10.1007/BF02362842zbMath0880.46021MaRDI QIDQ1912498

E. M. Vechtomov

Publication date: 12 May 1996

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

zbMATH Keywords

idealsrings of continuous functionsStone-Weierstrasssubringsspectra of ringssheaves of ringsGelfand-Kolmogorov, Gelfand-Shilovgerms of continuous functionsglobal sections of ringsrepresentation of algebraic objects as sets of functionsStone property

Mathematics Subject Classification ID

Associative rings of functions, subdirect products, sheaves of rings (16S60) Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) Research exposition (monographs, survey articles) pertaining to functional analysis (46-02) Algebraic properties of function spaces in general topology (54C40) Rings and algebras of continuous, differentiable or analytic functions (46E25)

Related Items (5)

Semirings of continuous functions ⋮ Lambek functional representation of generalized symmetric semirings ⋮ Functional representations of semirings. ⋮ Semifields and their properties ⋮ The principal kernels of semifields of continuous positive functions

Cites Work

• Compact ringed spaces
• Some remarks on p-rings and their Boolean geometry
• Projective topological spaces
• A structure theory for a class of lattice-ordered rings
• Representations of distributive lattices as lattices of functions
• Space of minimal prime ideals of a ring without nilpotent elements
• Localizations and adjointness
• On the Baer rings
• Projectivity of pure ideals
• More topologies on the torsion-theoretic spectrum of a ring
• Locales in functional analysis
• Prime and maximal ideals in subrings of C(X)
• Projective modules over rings of global sections of flasque sheaves
• Compact representations - the lattice theory of compact ringed spaces
• K-theory of function rings
• Recovering a frame from its sheaves of algebras
• Self-injective simple Pierce sheaves
• Algebra in a localic topos with applications to ring theory
• Categories of Boolean sheaves of simple algebras
• Structure spaces of rings and Banach algebras
• The affine scheme associated to a non-Noetherian prime PI algebra
• A Positivstellensatz for rings of continuous functions
• Isomorphic sheaf representations of normal lattices
• Local cohomology and quasicoherent sheaves
• K-theory of Gelfand rings
• M-structure and the Banach-Stone theorem
• Prime ideals and automatic continuity in algebras of differentiable functions
• Reticulated rings
• Compactifications determined by subsets of C*(X)
• Non-archimedean Gelfand theory
• Non-commutative algebraic geometry. An introduction
• Divisibility on countably dense ideals and countable orthocompleteness of modules
• A generalisation of Gel'fand duality
• Prime strict ideals in Rickart *-rings
• Multiplicative semigroups of continuous mappings
• On semigroups of continuous transformations of fuzzily structured sets
• Noncommutative rings in which every prime ideal is contained in a unique maximal ideal
• Function algebras on which homomorphisms are point evaluations on sequences
• Prime spectra in non-commutative algebra
• Compact convergence and the order bidual for C(X)
• Triple and sheaf representations of Stone lattices
• Noncommutative localization and sheaves
• Maximal ideals in algebras of topological algebra valued functions
• Projective quasi-coherent sheaves of Modules
• The maximal ideal space of a Noetherian ring
• Monadic algebras with finite degree
• Representation of regular rings of finite index
• An application of compactifications: Some theorems of maximal ideals
• A structure sheaf for a noncommutative Noetherian ring
• On an exact sequence of modules
• The Gelfand-Naimark theorems for \(C^*\)-algebras
• On the compactness of minimal spectrum
• Groupes et anneaux reticules
• Commutative non-Archimedean \(C^*\)-algebras
• The lattice of global sections of sheaves of chains over Boolean spaces
• A remark on the prime stalk theorem
• Some abstract maximal ideal-like spaces
• Spaces of vector-valued continuous functions
• Wallman rings
• A sheaf theoretic representation of rings with Boolean orthogonalities
• Strong De Morgan's law and the spectrum of a commutative ring
• Heredity of tensor products of topological algebras
• On the Stone-Weierstrass approximation theorem for valued fields
• E-kompakte Räume. (E-compact spaces)
• On nonarchimedian Banach algebras
• On regular nonarchimedian Banach algebras
• Spectral theory of algebras and adjunction of identity
• The Stone-Weierstrass theorem for valuable fields
• Non-Archimedean Gelfand theory
• The class of k-compact spaces is simple
• Generalization of Kaplansky's and Shirota's theorems on k-compact spaces
• The representation of biregular rings by sheaves
• Compact spaces of minimal prime ideals
• The structure space of a commutative locally M-convex algebra
• Some conditions on commutative semiprime rings
• Local cohomology. A seminar given by A. Grothendieck, Harvard University, Fall 1961. Notes by R. Hartshorne
• A representation theorem for certain connected rings
• On semigroups of functions on topological spaces
• Representation of l-groups and f-rings
• Gelfand and Wallman-type compactifications
• Non-Archimedean Banach algebras
• Pierce's representation and separable algebras
• On functional representations of topological algebras
• On a representation of a strongly harmonic ring by sheaves
• A condition for a ringed space to be a generator in its category of modules
• Lindelöf realcompactifications
• Representations by algebras of sections over Boolean spaces
• The product of F-spaces with P-spaces
• Category theory applied to Pontryagin duality
• Two characterizations of commutative Baer rings
• Topologies on the torsion-theoretic spectrum of a noncommutative ring
• Representation of semi-simple algebraic algebras
• An introduction to Nachbin spaces
• Co-elementary equivalence for compact Hausdorff spaces and compact abelian groups
• Algebraic subrings and perfect compactifications
• A representation of generalized Boolean rings
• On bicompact spaces
• Certain generalizations of the Weierstrass approximation theorem
• Normed algebras
• L'anneau spectral et l'anneau filtre d'homologie d'un espace localement compact et d'une application continue
• Modules over commutative regular rings
• The Maximal Ideal Space of a Ring of Measurable Functions
• Injective Hulls of C ∗ Algebras
• Extension of continuous functions in 𝛽𝐍
• An Elementary Construction in Sheaf Theory
• On rings of sets
• Representation of rings by sections
• Prime Ideal Structure in Commutative Rings
• A note on flasque sheaves
• Injective Hulls of C ∗ Algebras. II
• Measures on F-Spaces
• EXTREME POSITIVE OPERATORS
• Rings of Integer-Valued Continuous Functions
• A ring of analytic functions
• Couples spectraux et faisceaux associés. Applications aux anneaux de fonctions
• Prime z-Filters on Completely Regular Spaces
• What is a Sheaf?
• Algèbres Commutatives Engendrées Par Leurs Éléments Idempotents
• Singly Generated Homogeneous F-Algebras
• Commutative Rings in Which Every Prime Ideal is Contained in a Unique Maximal Ideal
• Representation of Abelian Groups and Rings by Families of Real-Valued Functions
• Remarks on Rings of Quotients of Rings of Functions
• Sur la compacité du spectre minimal d'un anneau
• The Minimal Prime Spectrum of a Commutative Ring
• On Functional Representations of a Ring without Nilpotent Elements
• On the Representation of Modules by Sheaves of Factor Modules
• Hereditary Commutative Rings and Centres of Hereditary Rings
• Intersections of Primary Ideals in Rings of Continuous Functions
• Structures Determined by Prime Ideals of Rings of Functions
• A Functor to Ringed Spaces
• Representations of presheaves of semiuniformisable spaces, and representation of a presheaf by the presheaf of all continuous sections in its covering-space
• Structures of continuous functions. I
• On topological algebra sheaves of a nuclear type
• Quotient Sheaves and Valuation Rings
• Representations of presheaves of closure space
• Representations of algebras by continuous sections
• A general character theory for partially ordered sets and lattices
• A note on E-compact spaces
• Normal lattices
• Note on a Subalgebra of C(X)
• A note on flabby sheaves
• Maximal Regular Right Ideal Space of a Primitive Ring
• The $\sigma$-Compact-Open Topology and its Relatives.
• Wallman-Type Compactifications on 0-Dimensional Spaces
• A Sheaf-Theoretic Duality Theory for Cylindric Algebras
• The Theory of Representation for Boolean Algebras
• Applications of the Theory of Boolean Rings to General Topology
• Topological representations of distributive lattices and Brouwerian logics
• Topological Representation of Algebras
• Rings of Real-Valued Continuous Functions. I
• Topological Rings
• The Weierstrass Theorem in Fields with Valuations
• Banach Algebras of Continuous Functions
• On a Theorem of Gelfand and Kolmogoroff Concerning Maximal Ideals in Rings of Continuous Functions
• A Topology for the Set of Primitive Ideals in an Arbitrary Ring
• Über nulldimensionale Räume
• Algebraic \(K\)-theory
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• Groups, Coverings and Galois Theory
• Spaces of ideals of distributive lattices II. Minimal prime ideals
• Sheaves of structures and generalized ultraproducts
• Rings of Continuous Functions with Values in a Topological Field
• Restricted Direct Products and Sectional Representations
• Dimension functions on the prime spectrum
• Model-completeness for sheaves of structures
• Pierce sheaves of non-commutative rings
• A structure sheaf for a noncommutative Noetherian ring
• N-Compactness and Weak Homogeneiety
• Stone lattices: a topological approach
• THE CONSTRUCTION OF SPACES DUAL TO PSEUDOCOMPLEMENTED DISTRIBUTIVE LATTICES
• Sheaves over the spectra of certain noncommutative rings
• Note on a Subring of C^*(X)⁽¹⁾
• A Sheaf Representation of Distributive Pseudocomplemented Lattices
• Discontinuous homomorphisms from 𝐶(𝑋)
• Semilattice theory with applications to point-set topology
• The Chinese remainder theorem and sheaf representations
• A topological structure on the structure shaf of a topological ring
• Addendum stalks of sheaves over the spectra of certain inionconmutative rings^∗
• An analogue of the pierce sheaf for non-commutative rings
• On Sheaf Representation of a Biregular Near-Ring
• Local Isomorphisms of Algebras of Continuous Functions
• The sheaf representation of near-rings and its applications
• Sheaves and normal submodels
• A Categorical Characterisation of Compactness
• The category of all zero-dimensional realcompact spaces is not simple
• Sheaf Constructions and Their Elementary Properties
• Sheaves and Boolean valued model theory
• Rings all of Whose Pierce Stalks are Local
• On a condition for the representability of a topological ring^∗∗
• A stucture sheaf for semiprime rings
• Prime Ideals in Uniform Algebras
• Prime Ideals and Sheaf Representation of a Pseudo Symmetric Ring
• Representation and extension of semiprime rings
• On Structure Spaces of Ideals In Rings of Continuous Functions
• Annulets and α-ideals in a distributive lattice
• On rings of sets II. Zero-sets
• The Structure Space of a Left Ideal.
• Quotient Frames and Subspaces
• The Space of Minimal Prime Ideals of a Commutative Ring
• On Wallman compactifications
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• \(p\)-rings and their boolean-vector representation
• The normal completion of a subset of a complete lattice and lattices of continuous functions
• Maximal ideals in rings of bounded continuous functions
• An isomorphism theorem for real-closed fields
• Azumaya rings, pierce stalks and central ideal algebras
• On the Gel'fand-Kolmogorov theorem on maximal ideals of rings of continuous functions
• Representation of positive semirings by sections
• Alexandroff Algebras and Complete Regularity
• Stonesche Körper und ein Überdeckungssatz
• Concerning spaces of continuous functions
• On Rings of Bounded Continuous Functions with Values in a Division Ring
• Ideals in A Certain Banach Algebra
• Rings with Hausdorff structure space
• The space of prime ideals of a ring
• Compactness of the Structure Space of a Ring
• Zur Idealtheorie der ganzen Funktionen. In memoriam Hermann Ludwig Schmid
• Characters of Cartesian Products of Algebras
• The trace of certain operators
• Prime Ideals in Vector Lattices
• On a Representation Theory for a Class of Archimedean Lattice-Ordered Rings
• Structural characterization of functional spaces
• Two dimensions defined on the spectrum of a noncommutative ring
• A Sheaf Representation for Modules with Applications to Gelfand Rings
• Torsion theoretic points and spaces
• On cerrain classes of pe-rings
• The Gelfand Subalgebra of Real or Nonarchimedean Valued Continuous Functions
• Arens Regularity of the Algebra C(K,A )
• Spectral spacess and non-commutative rings
• Sheaf representations of strongly harmonic rings
• Nonarchimedean C #(X)
• Sur quelques classes d'anneaux non commutatifs
• Real closed rings, I. Residue rings of rings of continuous functions
• Filtered sheaves and their localizations
• Tensor products of function algebras
• Characterising complete boolean algebras in terms of pure essentialness
• Sheaves with Finitely Generated Isomorphic Stalks and Homology Manifolds
• Vector Bundles and Projective Modules
• An ordered sheaf representation of subresiduated lattices
• The Duality of Distributive Continuous Lattices
• ON DERIVATIONALLY PRIME RINGS
• Injective Sheaves of Abelian Groups: A Counterexample
• On Characterizing Injective Sheaves: Corrigendum
• Ideal Theory in f-Algebras
• On pm-rings
• Banach Bundles of Continuous Functions and an Integral Representation Theorem
• Lattice Homomorphisms of Spaces of Continuous Functions
• Extensions and localization
• The lambek sheaf reexamined

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