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

The Hilbert ideal is the ideal generated by positive degree invariant polynomials of a finite group. For a cyclic group of prime order p, we show that the image of the transfer lie in the ideal generated by invariants of degree at most p−1. Consequently we show that the Hilbert ideal corresponding to an indecomposable representation is generated by polynomials of degree at most p, confirming a conjecture of Harm Derksen and Gregor Kemper for this case.