Structure sheaves and noncommutative topologies
The main purpose of this paper is to construct structure sheaves over noncommutative topologies associated to an arbitrary left noetherian ring. In the first section the authors quickly recollect some of the main notions, constructions and results, which will be needed throughout. In the second section, they study localization at elements in the free semigroup generated by all Gabriel filters over a fixed base ring and prove its main properties. In particular, they show how the main results of \textit{A. Verschoren} [J. Algebra 182, No. 2, 341-346 (1996; Zbl 0863.16024)] may be generalized to this set-up. In the last section, they introduce noncommutative topologies over an arbitrary ring and show how the former results may be applied to construct structure sheaves over these. Some examples are included, showing their methods to generalize previous sheaf constructions in the literature.
scientific article; zbMATH DE number 1053882
scientific article