On a conductor discriminant formula of MCCULLOH

 For each finite quasi-Frobenius ring E McCulloh has constructed an order T(E) in a Galois algebra over Q with Galois group E^∗. For E=Z/nZ the order T(E) is the cyclotomic ring Z[ζn]. This note addresses the conductor discriminant formula that McCulloh has proposed for these orders. For commutative E we show that one inequality holds and that we have equality if and only if E is a principal ideal ring.