摘要
Szasz FA提出下列两个公开问题.(1)求根性R对任意环A和A的任意两个理想I_1,I_2满足R(I_1+I_2)=R(I_1)+R(I_2)的充分必要条件(即Szasz的问题12).(2)求根性R对任意环A和A的任意两个理想I_1,I_2满足(I_1∩I_2)=I_1∩I_2的充分必要条件(即Szasz的问题13).本文引入σ—根和τ—根,利用σ—根和τ—根分别给出了上述两个问题的充分必要条件.
Szasz FA has put forword two open problems:
Problem 12: How can a necessary and sufficient condition be formulated for a radical property R in order that R(I1)+R(I2)=R(I1+I2)should always be valid for arbitrary ideals I1 and I2 of an arbitrary ring?
Problem 13:How can a necessary and sufficient condition be formulated for a radical property R in order that (I1∩I2)= Γ1∩Γ2 should always be valid for arbitrary ideals I1and I2 of an arbitrary ring?
This note has given some results of the two problems.
出处
《云南大学学报（自然科学版）》
CAS
CSCD
1990年第2期107-112,共6页
Journal of Yunnan University(Natural Sciences Edition)
关键词
环
理想
根
结合环
-根
-根
δ radical,complete δ radical,τ radical,complete τ radical,hereditary radical,strong semisimplicity
