Noncommutative Pierce duality between Steinberg rings and ample ringoid bundles

0572039 - MÚ 2024 RIV NL eng J - Journal Article
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
R&D Projects: GA ČR(CZ) GF22-07833K
Institutional support: RVO:67985840
Keywords : ringoid bundle * Steinberg algebra * Étale groupoid
OECD category: Pure mathematics
Impact factor: 0.8, year: 2022
Method of publishing: Limited access
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.
Permanent Link: https://hdl.handle.net/11104/0342880