A Sheaf Representation for Modules with Applications to Gelfand Rings

DOI10.1112/PLMS/S3-48.2.230zbMath0536.18003OpenAlexW1999418184MaRDI QIDQ3320571

Gilberte van den Bossche, Harold Simmons, Francis Borceux

Publication date: 1984

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/plms/s3-48.2.230

zbMATH Keywords

maximal spectrumGelfand ringsright pure idealslocale of virginal idealsMulvey representationsheaf representation for modules over ring

Mathematics Subject Classification ID

Category-theoretic methods and results in associative algebras (except as in 16D90) (16B50) Topoi (18B25) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20) Representation theory of associative rings and algebras (16Gxx) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items (18)

Sheaf representations and graded manifolds ⋮ Rings of continuous functions and their maximal spectra ⋮ Isomorphic sheaf representations of normal lattices ⋮ Gelfand Factor Rings and Weak Zariski Topologies ⋮ An algebraic construction for integral Čech cohomology ⋮ Rings and sheaves ⋮ Rings of continuous functions with values in a topological division ring ⋮ Reticulation of a quantale, pure elements and new transfer properties ⋮ Attaching topological spaces to a module. I: sobriety and spatiality ⋮ On strongly harmonic and Gelfand modules ⋮ Functional representations of semirings. ⋮ On purely-prime ideals with applications ⋮ Rings in which every prime ideal is contained in a unique maximal right ideal ⋮ Some abstract maximal ideal-like spaces ⋮ Spectra of Maximal 1-Sided Ideals and Primitive Ideals ⋮ A stucture sheaf for semiprime rings ⋮ Sheaf representations of strongly harmonic rings ⋮ Rickart residuated lattices

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