Prime Decompositions of Radicals in Polynomial Rings

Michael Kalkbrener
1994 Journal of symbolic computation  
In this paper we are concerned with the computation of prime decompositions of radicals in polynomial rings over a noetherian commutative ring R with identity. We show that prime decomposition algorithms in R can be lifted to R[x] if for every prime ideal P in R univariate polynomials can be factored over the quotient field of the residue class ring R/P . In the proof of this result a lifting algorithm is constructed which can be considered as a generalization of the algorithm of Ritt and Wu.
more » ... ample: Let R be the multivariate polynomial ring K[x 1 , . . . , x n ] over a field K
doi:10.1006/jsco.1994.1052 fatcat:36lszgijy5hnhib56ckk4swolq