半环的J-根

本支对半环引进J-根的概念,给出了其半模的刻划,证明了它是一个根性。同时讨论了由J(∧)导出的环K(J(∧))与由半环八导出的环K(∧)的Jacobson根J(K(∧))的关系。

关于由J-半单的亚直不可约环类所确定的刻划

[1]中定义由J-半单的亚直不可约环类所确定的上根R,并给出了一个环为R-根环的几个等价条件。另给出了一些刻划,最后证明了对任意环A,R（An）=[R（A）]n.

关于半群分次环

设H 是有单位元e 的半群,G是H 的最大子群,Jg(A) 和Jg(S) 分别是A 和S的分次J-根.证明了Jg(A)= Jg(S) (τ∈HwGAτ),讨论了环B的左自内射性与半群环BH

The Upper Radical Determined by the Class of all J-Semisimple Subdirectly Irreducible Rings

F.A.Szasz has put forward the open problem 55 in [1]: Let K be the class of all subdirectly irreducible rings, whose Jacobson radical is (0). Examine the upper radical determined by the class K. In this paper, the problem has been examined. (1) It has been proved that the upper radical R determined by the class K is a special radical,which lies between Jacobson radical and Brown-McCoy radical. (2) It has been given some necessary and sufficient condition of ring A to be an R-radical ring.