General Radicals that Coincide with the Classical Radical on Rings with D.C.C

General radical theories were obtained by Amitsur (1; 2; 3) and Kurosh (6). Following Kurosh we say that a property of rings is a radical property if: (a) Every homomorphic image of an -ring is an -ring; (b) Every ring R contains an -ideal S which contains every other -ideal of R; (c) The factor ring R/S is -semi-simple (that is, has no non-zero -ideals).