Primary Decomposition: Algorithms and Comparisons

The Hilbert series and degree bounds play significant roles in computational invariant theory. In the modular case, neither of these tools is avrulable in general. In this article three results are obtruned, which provide partial remedies for these shortcomings. First, it is shown that the so-called extended Hilbert series, which can always be calculated by a MoHen type formula, yields strong constraints on the degrees of primary invariants. Then it is shown that for a trivial source module the (ordinary) Hilbert series coincides with that of a lift to characteristic 0 and can hence be calculated by MoHen’s formula. The last result is a generalization of Goobel’s degree bound to the case of monomial representations.

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