模的Total根以及零Total的模

Total of Modules and Modules With Zero Total

模的Total根包含模的Jacobson根,并且满足Tot(MR)+J(MR) Tot(MR).特别的零Total的模是一个半素模,零Total的模类是一个弱特别模类,从而零Total的环类为弱特别环类,其上根为超级幂零根.

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.