Quasi-\(P\) radicals of associative rings (Q1207359)

The author introduces the notions of quasi-\(P\) rings, quasi-\(P\) ideals and quasi-\(P\) radicals. He points out that if \(P\) is a property of rings, for instance, nilpotent property, local nilpotent property, nil property etc., then the corresponding radicals such as the quasi-nilpotent radical, quasi-local nilpotent radical, quasi-nil radical etc. can be obtained. He shows that a quasi-\(P\) radical of \(R\) is the same as a \(P\)- radical if \(P\) is a radical property. Moreover, all quasi-\(P\) radicals are Amitsur-Kurosh radicals. A number of results on radicals of associative rings are unified by quasi-radicals.