Hiroshima Math. J. 34 (2004), 1–19 Kernels of derivations in positive characteristic

Abstract. Let R be an integral domain that is finitely generated over a field k. Let D: R! R be a derivation over k. Our aim is to compute Ker D. Under the assumptions that the characteristic of k is zero, D is locally nilpotent and Ker D is finitely generated over k, Essen gave an explicit algorithm based on the exponential of the derivation. In this paper we give an analogous algorithm in the positive characteristic case using a truncated version of the exponential. It does not require the nilpotence of D. We give several computational examples of application of our algorithm. Also using higher derivations, we obtain a word-by-word translation of Essen’s formula to positive characteristics. 1