Computing a Grobner basis of a polynomial ideal over a principal domain
Ihsen Yengui · 2005
The purpose of this paper is to give a simple decision procedure for the ideal membership problem for polynomial rings over principal domains. As a particular case, we solve a fundamental algorithmic question in the theory of multivariate polynomials over the integers called \Kronecker’s problem, that is the problem of flnding a decision procedure for the ideal membership problem for Z[X1;:::;Xn]. The techniques utilized are easily generalizable to Dedekind domains.