On the D-bases of polynomial ideals over principal ideal domains (Q1118398)

D-reductions in a polynomial ring are similar to B-reductions arising in producing Gröbner bases. More generally than B-reductions, D-reductions are valid for principal ideal domains (as a ring of coefficients). An algorithm for reducing to D-bases of a polynomial ideal which is similar to critical-pair/completion algorithm is described. It is proved that over rings of polynomials with coefficients in an euclidean domain the notions of B-bases and D-bases coincide.