On the Amitsur property of radicals

N. V. Loi, R. Wiegandt


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.


Amitsur property, hereditary, normal and generalized nil radical

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