Parallelization of modular algorithms (Q2430024)

The title is a bit of an understatement, the results are also interesting without parallelisation. First, a modular algorithm for the computation of Gröbner bases is given. Its correctness was shown in [\textit{E. A. Arnold}, ``Modular algorithms for computing Gröbner bases'', J. Symb. Comput. 35, No. 4, 403-419 (2003; Zbl 1046.13018)] for the homegeneous case and in [\textit{G.-M. Greuel, G. Pfister}, A Singular Introduction to Commutative Algebra. Berlin: Springer. (2007; Zbl 1133.13001)] for local orderings; here the case of global orderings is treated. Also, the paper contains a modular algorithm for the computation of associated primes of zero-dimensional ideals.