A note on the Hilbert ideals of a cyclic group of prime order (Q2468536)

The Hilbert ideal of the algebra of invariant polynomials of a representation of a finite group is the ideal generated by the positive degree polynomials. \textit{H. Dirksen} and \textit{G. Kemper} [``Computational invariant theory.'' Encyclopaedia of Mathematical Sciences. Invariant Theory and Algebraic Transformation Groups. 130(1) (2002; Zbl 1011.13003)] conjectured that the Hilbert ideal is generated by homogeneous elements of degree at most \(| G| \). Here the author confirms this conjecture in the modular case for \(G\) cyclic of prime order \(p\).