PRIME DECOMPOSITIONS OF RADICALS IN POLYNOMIAL-RINGS

In this paper we are concerned with the computation of prime decomposi tions of radicals in polynomial rings over a noetherian commutative ri ng R with identity. We show that prime decomposition algorithms in R c an be liked to R[x] if for every prime ideal P in R univariate polynom ials can be factored over the quotient field of the residue class ring R/P. In the proof of this result a liking algorithm is constructed wh ich can be considered as a generalization of the algorithm of Ritt and Wu.