2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68582Let (R,m,k) be an excellent local ring of positive prime characteristic. We show that if Tor_1^R(R^+,k) = 0 then R is regular. This improves a result of Schoutens, in which the additional hypothesis that R was an isolated singularity was required for the proof.3 pages, to appear in Proceedings of the AMSCommutative Algebra13A35; 13H05text