Abstract
We construct a nil ring R which has bounded index of nilpotence 2, is Wedderburn radical, and is commutative, and which also has a derivation δ for which the differential polynomial ring R[x;δ] is not even prime radical. This example gives a strong barrier to lifting certain radical properties from rings to differential polynomial rings. It also demarcates the strength of recent results about locally nilpotent PI rings.
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