Abstract
ABSTRACT We show that the relation ideal of a univariate polynomial with Galois group G is generated by G-invariant relations; these relations arise from an arbitrary set of generators of the invariant ring of G in a natural way. When G is the symmetric group, the most obvious generators of this kind form an H-basis (in the sense of Macaulay) of the relation ideal. This means that there is an effective way to write any given relation in terms of these generators. We further show that such a result cannot be expected to hold for the alternating group.
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