α-GWCN 环

Study on α-GWCN Rings

作为GWCN环的推广,提出了α-GWCN环的概念,讨论了它与一些特殊环的关系,给出了α-GWCN环的一些性质.证明了:设R为环,I为R的理想,α(I)≤I,则有1)若I≤N(R),R为α-GWCN环,那么R/I为α-GWCN环;2)若I是约化的,且R/I是α-GWCN环,那么R为α-GWCN环.其中α:R/I→R/I,α(a+I)=α(a)+I,任意a∈R.

In this study, GWCN rings were promoted and the concept of the α-GWCN rings was also introduced. The relationships between α-GWCN rings and other special rings were explored and some properties of α-GWCN rings were put forward. And the result that let R be a ring, I is an ideal of R, α（I）≤I, then 1）if I≤N（R） and R is an α-GWCN ring, then R/I is α-GWCN;2）if I is reduced and R/I is an α-GWCN ring, then R is α-GWCN, with α： R/I →R/I, α（a ＋ I） = α（a） ＋ I for all a∈R.