%0 Journal Article %A Norton, G.H. %A Salagean, Ana %D 2006 %T Gröbner bases and products of coefficient rings %U https://repository.lboro.ac.uk/articles/journal_contribution/Gr_bner_bases_and_products_of_coefficient_rings/9402641 %2 https://repository.lboro.ac.uk/ndownloader/files/17019221 %K untagged %K Information and Computing Sciences not elsewhere classified %X Suppose that A is a finite direct product of commutative rings. We show from first principles that a Gröbner basis for an ideal of A[x1,..., xn] can be easily obtained by ’joining’ Gröbner bases of the projected ideals with coefficients in the factors of A (which can themselves be obtained in parallel). Similarly for strong Gröbner bases. This gives an elementary method of constructing a (strong) Gröbner basis when the Chinese Remainder Theorem applies to the coefficient ring and we know how to compute (strong) Gröbner bases in each factor. %I Loughborough University