DETECTING UNNECESSARY REDUCTIONS IN COMPUTING GR¨OBNER BASES OVER GALOIS RINGS

Byrne and Fitzpatrick in [2] have presented an algorithm for computing Gr¨obner bases over Galois rings. But they have not used Buchberger’s criteria in their algorithm to avoid unnecessary reductions. In this paper, we propose the adapted versions of these criteria for polynomials over Galois rings for detecting unnecessary reductions.