Noncommutative Localizations of Lie-Complete Rings

Date

2016-01-01

Author

Dosi, Anar

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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 is an element of A is embedded into the ring O-A (X-f) of all sections of the structure sheaf O-A on the principal open set X-f as a dense subring with respect to the weak I-1-adic topology, where I-1 is the two-sided ideal generated by all commutators in A. The equality A((f)) = O-A (X-f) can only be achieved in the case of an NC-complete ring A.

Subject Keywords

Lie-Nilpotent Ring, Noncommutative Affine Scheme, Noncommutative Localization

URI

https://hdl.handle.net/11511/63693

Journal

COMMUNICATIONS IN ALGEBRA

DOI

https://doi.org/10.1080/00927872.2015.1130135

Collections

Natural Sciences and Mathematics, Article

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Citation Formats

A. Dosi, “Noncommutative Localizations of Lie-Complete Rings,” COMMUNICATIONS IN ALGEBRA, pp. 4892–4944, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63693.