On the Amitsur property of radicals - Loi, N.V.; Wiegandt, R. (Algebra and Discrete Mathematics, 2006)
The Amitsur property of a radical says that
the radical of a polynomial ring is again a polynomial ring. A
hereditary radical γ has the Amitsur property if and only if its
semisimple class is polynomially extensible and satisfies: f(x) ∈
γ(A[x]) implies f(0) ∈ γ(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.