Noncommutative Pierce duality between Steinberg rings and ample ringoid bundles

0572039 - MÚ 2024 RIV NL eng J - Článek v odborném periodiku
Bice, Tristan
Noncommutative Pierce duality between Steinberg rings and ample ringoid bundles.
Journal of Pure and Applied Algebra. Roč. 227, č. 11 (2023), č. článku 107407. ISSN 0022-4049. E-ISSN 1873-1376
Grant CEP: GA ČR(CZ) GF22-07833K
Institucionální podpora: RVO:67985840
Klíčová slova: ringoid bundle * Steinberg algebra * Étale groupoid
Obor OECD: Pure mathematics
Impakt faktor: 0.8, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.jpaa.2023.107407

Classic work of Pierce and Dauns-Hofmann shows that biregular rings are dual to simple ring bundles over Stone spaces. We extend this duality to Steinberg rings, a purely algebraic generalisation of Steinberg algebras, and ringoid bundles over ample groupoids. We base this largely on an even more general extension of Lawson's noncommutative Stone duality, specifically between Steinberg semigroups, a generalisation of Boolean inverse semigroups, and category bundles over ample groupoids.
Trvalý link: https://hdl.handle.net/11104/0342880