分次Γ环在升链条件下的性质及其PG根

在Γ环的基础上给出群分次Γ环及分次Γ理想等相关 概念, 得到分次Γ环的某些重要性质. 证明分次情况下的Levitizki定理、 Xie定理和Herstein-Small定理; 并通过定义分次P_G根、 分次WP_G根和分次QPG根, 推广了在Γ环中的相关结论.

Properties of Graded Γ-Rings Satisfing Certain Chain Conditionsand Its PG-Radical

The present paper presents the concepts of group graded Γ-rings and graded Γ-ideals on the basis of the concept of Γ-rings and the obtained some important properties of group graded Γ-rings. By proving Levitizki’s theorem, Xie’s theorem and Herstein-Small’s theorem, e tc., and defining P_G-radical, WP_G-radical and QP_{G-radical, we draw the conclusions which are already true in Γ-rings.}