Г-环的强Levitzki根与拟强Levitzki根

The Locally Strong Nilpotent Radical and Quasi Locally Strong Nilpotent Radical of Г-ring

本文定义了Γ-环的局部强幂零理想与拟局部强幂零理想,研究了局部强幂零根与拟局部强幂零根,并且证明了任何Γ-环都有拟局部强幂零根,且拟局部强幂零根等于局部强幂零根。

In this paper,we defined the concept of the locally strong nilpotent ideal and the quasi locally strong nilpotent ideal of Г-ring,and studied locally strong nilpotent radical and quasi locally strong nilpotent radical.The main resultes in this paper are: Let M be any Г-ring,it must have a quasi locally strong nilpotent radical L_Q,and M/L_Q is quasi locally strong nilpotent semi simple. For any Г-ring M,its locally strong nilpotent radical equals quasi locally strong nilpotent radical.