On the maximal Kurosh-Amitsur model for the Wedderburn-Artin radical (Q1324776)

Consider an associative ring in which the sum of the nilpotent ideals is nilpotent. Let \(W\) denote the unique maximal nilpotent ideal of the ring. The nilpotency of rings does not define a Kurosh-Amitsur radical in the class of all associative rings. However, in a hereditary and homomorphically closed class of rings with nilpotent radical, the nilpotency does define a Kurosh-Amitsur radical. In this paper, the authors investigate the relationship between the radical \(W\) of the class of all rings with nilpotent radical and the general radicals of the class of all associative rings.