2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163485A close connection between the no-name lemma (concerning algebraic groups acting on vector bundles) and the existence of sufficiently many independent rational covariants is pointed out. In particular, this leads to a new natural proof of the no-name lemma. For linearly reductive groups, the approach has a refined variant based on integral covariants. This fits into the usual context of invariant theory, and yields a version of the no-name lemma that has a constructive nature.The paper has been completely rewritten, more conclusive results are achievedRepresentation TheoryAlgebraic Geometry13A50; 14L30; 20G05text