Ring theory and pointfree topology.

DOI10.1016/S0166-8641(03)00196-2zbMath1040.06004OpenAlexW1967639792MaRDI QIDQ1426502

Bernhard Banaschewski

Publication date: 14 March 2004

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

Full work available at URL: https://doi.org/10.1016/s0166-8641(03)00196-2

zbMATH Keywords

exchange ringordered ringsGelfand ringsheaf representation theorysheaves on locales

Mathematics Subject Classification ID

Frames, locales (06D22) Ordered rings, algebras, modules (06F25) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20) Axiom of choice and related propositions (03E25) Ordered rings (13J25) General commutative ring theory (13A99)

Related Items (9)

Feebly projectable algebraic frames and multiplicative filters of ideals ⋮ Barr-exact categories and soft sheaf representations ⋮ Classes of commutative clean rings ⋮ Ideals in the Ring of Colombeau Generalized Numbers ⋮ A natural equivalence for the category of coherent frames ⋮ Ring ideals and the Stone-Čech compactification in pointfree topology ⋮ \(z\)-ideals in the real continuous function ring \(\mathcal{R}(L_{\tau}) \) ⋮ On feckly clean rings ⋮ Algebras of generalized functions with smooth parameter dependence

Cites Work

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• On the localic Yosida representation of an archimedean lattice ordered group with weak order unit
• The prime ideal theorem and representation of \(F\)-rings
• A generalisation of Gel'fand duality
• Exchange rings and decompositions of modules
• A globalisation of the Gelfand duality theorem
• The spectral theory of commutative C^∗-algebras: The constructive spectrum
• The spectral theory of commutative C^∗-algebras: The constructive Gelfand-Mazur theorem
• Lattice Aspects of Radical Ideals and Choice Principles
• Frames Associated with an Abelian l-Group
• Lifting Idempotents and Exchange Rings
• Recent Results in Pointfree Topology
• Commutative Rings in Which Every Prime Ideal is Contained in a Unique Maximal Ideal
• A Characterization of Exchange Rings
• \(f\)-rings and the Stone-Weierstrass theorem

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