Let d be a K-derivation of the polynomial ring K[x1, ..., x n] over a field K of characteristic 0, and let d̃ be the extension of d to the fraction field K(x1, ..., xn). Recently Ayad and Ryckelynck proved that if the kernel Ker d of d contains n - 1 algebraically independent polynomials then Ker d̃ is equal to the fraction field Q(Ker d) of Ker d. In this note, we give a short proof for this result. Copyright © Taylor &amp
Francis, Inc.