2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121588It is shown that a Hopf algebra over a field admitting a Galois extension separable over its subalgebra of coinvariants is of finite dimension. This answers in the affirmative a question posed by Beattie et al. in [{\it Proc. Amer. Math. Soc.} 128 No. 11 (2000), 3201-3203].Some typos corrected. Minor grammatical changes. A new result and reference addedSymplectic GeometryRings and Algebras16W30text