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If a property P of ring elements satisfies conditions (a)-(d), then the largest homomorphically closed class having no non-zero /"-element is a dual radical in the sense of AndrunakieviC, and every dual radical can be obtained in this way. Also properties defined by polynomials are considered and as an application we get various characterizations of the Behrens radical. 1980 Mathematics subject classification (Amer. Math. Soc): 16 A 21.doi:10.1017/s1446788700029761 fatcat:o2flku26lrhq7ph6m6hmivmykm