2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64389We show how to express any Hasse-Schmidt derivation of an algebra in terms of a finite number of them under natural hypothesis. As an application, we obtain coefficient fields of the completion of a regular local ring of positive characteristic in terms of Hasse-Schmidt derivations14 pages; A gap in the statement of Proposition (2.7) has been fixed and the proof of Theorem (3.14) has been adaptedCommutative Algebra13H05 (Primary) 13N15, 13N10, 13A35 (Secondary)text