Rings and sheaves (Q1912498)
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scientific article; zbMATH DE number 877634
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Rings and sheaves |
scientific article; zbMATH DE number 877634 |
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Rings and sheaves (English)
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12 May 1996
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This paper is a sequel to the author's earlier survey [Itogi Nauki Tekh., Ser. Algebra, Topologiya, Geom. 29, 119-191 (1991; Zbl 0835.54019)] whose goal is the representation of algebraic objects as sets of functions. Chapter 1 is a historical essay on some of the main theorems in rings of continuous functions, including those of Gelfand-Kolmogorov, Gelfand-Shilov, and Stone-Weierstrass. He also discusses ideals and subrings, including those of Gelfand and Wallman, as well as duality theorems and the Stone property. Chapter 2 is a historical essay and survey of sheaves of rings, leading to sheaves of rings of germs of continuous functions, as well as the spectra of rings. Chapter 3 treats the general theory of sheaf representations of rings, including those of Pierce and Lambek, among others. The survey ends with a bibliography of 550 items.
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global sections of rings
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representation of algebraic objects as sets of functions
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rings of continuous functions
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Gelfand-Kolmogorov, Gelfand-Shilov
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Stone-Weierstrass
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ideals
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subrings
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Stone property
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sheaves of rings
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germs of continuous functions
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spectra of rings
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