On the Amitsur property of radicals

The Amitsur property of a radical says that the radical of a polynomial ring is again a polynomial ring. A hereditary radical $\gamma$ has the Amitsur property if and only if its semisimple class is polynomially extensible and satisfies: $f(x)\in\gamma(A[x])$ implies $f(0)\in\gamma(A[x])$. Applying this criterion, it is proved that the generalized nil radical has the Amitsur property. In this way the Amitsur property of a not necessarily hereditary normal radical can be checked.