Abstract
In this paper, we give an algorithm that computes syzygies over Laurent polynomials ring: R[X-1(+/- 1),..., X-n(+/- 1)], with R is a valuation ring (R a valuation domain of any Krull dimension) which neither relies on Noetherianity nor on Krull dimension. The idea is based on the isomorphism R[X-1(+/- 1), ..., X-n(+/- 1)] congruent to R[X-1, ..., X-n Y/< X-1 ... XnY - 1 >] and the syzygy computation over the polynomials ring R[X-1, ..., X-n]. At the end of this paper, we prove that this algorithm is also valid for Prufer domain.