Computing the radical of an ideal in positive characteristic

We propose a method for computing the radical of an arbitrary ideal in the polynomial ring in n variables over a perfect field of characteristic p>0, In our method Buchberger's algorithm is performed once in n variables and a Grobner basis conversion algorithm is performed at most [n log(p) d] times in 2n variables, where d is the maximum of total degrees of generators of the ideal and 3. Next we explain how to compute radicals over a finitely ge nerated coefficient field over a field K, when we have a radical computatio n method over the field K. Thus we can compute radicals over any finitely g enerated field over a perfect field. (C) 2001 Academic Press.