Abstract

AbstractLet$\alpha $be any radical of associative rings. A radical$\gamma $is called$\alpha $-like if, for every$\alpha $-semisimple ring$A$, the polynomial ring$A[x] $is$\gamma $-semisimple. In this paper we describe properties of$\alpha $-like radicals and show how they can be used to solve some open problems in radical theory.

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