Noncommutative Localizations of Lie-Complete Rings
| Autor: | Anar Dosi |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Principal ideal ring
Discrete mathematics Reduced ring Ring (mathematics) Pure mathematics Algebra and Number Theory Noncommutative ring Mathematics::Commutative Algebra 010102 general mathematics Commutative ring 01 natural sciences Localization of a ring 0103 physical sciences Topological ring Noncommutative algebraic geometry 010307 mathematical physics 0101 mathematics Mathematics |
| Zdroj: | Communications in Algebra. 44:4892-4944 |
| ISSN: | 1532-4125 0092-7872 |
| DOI: | 10.1080/00927872.2015.1130135 |
| Popis: | In this paper we investigate the topological localizations of Lie-complete rings. It has been proved that a topological localization of a Lie-complete ring is commutative modulo its topological nilradical. Based on the topological localizations we define a noncommutative affine scheme X = Spf(A) for a Lie-complete ring A. The main result of the paper asserts that the topological localization A(f) of A at f ∈ A is embedded into the ring 𝒪A(Xf) of all sections of the structure sheaf 𝒪A on the principal open set Xf as a dense subring with respect to the weak I1-adic topology, where I1 is the two-sided ideal generated by all commutators in A. The equality A(f) = 𝒪A(Xf) can only be achieved in the case of an NC-complete ring A. |
| Databáze: | OpenAIRE |
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