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On \(A\)-radicals. (English) Zbl 1150.16018
A Kurosh-Amitsur radical \(\gamma\) of rings is said to be an \(A\)-radical if for any two rings \(A,B\) with isomorphic additive groups \(A\in\gamma\Rightarrow B\in\gamma\).
Some necessary and sufficient conditions characterizing radicals \(\gamma\) which are \(A\)-radicals are proved in this paper. These conditions are formulated in terms of the properties of quasi-ideals of rings \(A\in\gamma\).
MSC:
16N80 General radicals and associative rings
16D25 Ideals in associative algebras
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References:
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