Geodesic
On the Amitsur property of radicals
Algebra and discrete mathematics, no. 3 (2006), pp. 92-100

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: Amitsur property, hereditary, normal and generalized nil radical. 
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     title = {On the {Amitsur} property of radicals},
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N. V. Loi; R. Wiegandt. On the Amitsur property of radicals. Algebra and discrete mathematics, no. 3 (2006), pp. 92-100. http://geodesic.mathdoc.fr/item/ADM_2006_3_a7/