Abstract: Total of modules contain Jacobson radicals, and Tot ( M_R ) + J ( M_R ) ?? Tot ( M_R ) for a right R- module. In particular, a module with zero Total is a semiprime module and the class of such modules is a weakly special class. So the class of rings with zero Total is a weakly special class and the upper radical of this class is a supernilpotent radical.

Key words: Total, idempotent, weakly special class