Abstract
The constructions for the lower radical class, the upper radical class, and the smallest semisimple class were introduced in 1953 by KUROSH. Generalizations of the lower radical class and smallest semisimple class constructions were given in 1970 by LEAVITT. Here these constructions are investigated in the presence of two universal classes. The result of KUROSH for the lower radical construction is generalized and similar results are obtained for the other constructions.
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