2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119809Let k be an algebraically closed field of characteristic zero. We show that the centre of a homologically homogeneous, finitely generated k-algebra has rational singularities. In particular if a finitely generated normal commutative k-algebra has a noncommutative crepant resolution, as introduced by the second author, then it has rational singularities.Algebraic GeometryRings and Algebras14A22, 14E15, 16S38text