Applying Buchberger's criteria for computing Gröbner bases over finite-chain rings (Q2853970)

The authors of this paper prove a version of Buchberger's criteria for Gröbner bases over finite-chain rings, i.e. rings which have only finitely many ideals. Moreover, they generalize the algorithm for the computation of Gröbner bases over Galois rings, i.e. special finite-chain rings, as introduced in [\textit{E. Byrne} and \textit{P. Fitzpatrick}, J. Symb. Comput. 31, No. 5, 565--584 (2001; Zbl 1030.94047)] to arbitrary finite-chain rings. They also show that their version of Buchberger's criteria can be effectively implemented in this generalized algorithm. At last, they give some examples that show that Buchberger's criteria significantly ease the computation of Gröbner bases over Galois rings.