几乎强幂零Γ-环所确定的根

Radicals Determined by the Class of Almost Strongly Nilpotent Γ-rings

本文讨论几乎强幂零Γ-环及其所确定的根。主要证明了:(1)Γ-环的素根类是几乎强幂零Γ-环类的最小划分;(2)由一切几乎强幂零Γ-环类所确定的下根重合于由一切无非零几乎强幂零理想的Γ-环所确定的上根。

In this paper, the notion of strongly nilpotent Γ-rings is generalized by introducing the class of almost strongly nilpotent Γ-rings, that is, of Γ-rings every proper Γ-homomorphie image of which, is strongly nilpotent Γ-ring, the simple Γ-ring are assumed not to be almost strongly nilpotent, and following results are proved:(Ⅰ) the prime radical class is the smallest one of all partitions containing nonzero almost strongly nilpotent Γ-rings of the class of almost strongly nilpotent Γ-rings.(Ⅱ)the lower radical property determined by the class of all almost strongly nilpotent Γ-rings Coineids with the upper radical property determined by the class of all Γ-rings without nonzero almost strongly nilpotent ideals.