Kernels of derivations in positive characteristic
This paper deals with the kernels of derivations in positive characteristic. Let \(R\) be an integral domain that is finitely generated over a field \(k\). Let \(D:R\rightarrow R\) be a derivation over \(k\). In J. Symb. Comput. 16, 551--555 (1993; Zbl 0809.13002) \textit{A. van den Essen} gives an explicit algorithm to compute the derivation kernel when the characteristic of \(k\) is zero, \(D\) is locally nilpotent and \(\text{Ker\,}D\) is finitely generated. Here the author gives an algorithm to compute the derivation kernel in positive characteristic, inspired by van den Essen's algorithm, but using a truncated version of the exponential of the derivation. A key point in calculating the derivation kernel is to consider the derivation kernel as a \(k[R^p]\)-module. The algorithm can be implemented by the Singular software programme. The theoretical results are interpreted with the help of several interesting examples.
scientific article; zbMATH DE number 2111505