非交换环上的Zariski拓扑

Zariski Topology over a Noncommutative Ring

设R是任意带单位元的结合环,用素谱[Specl(R),Γ2(R)]的一些拓扑性质去刻画环的性质。对任意环R,用N(R)表示环R的素根,证明了:R/N(R)是强Harmonic环当且仅当[Specl(R),Γ2(R)]是正规空间。且建立了[Specl(R),Γ2(R)]的开闭集与环R的幂等元之间的关系。

Let R be any associative ring with identity. In this paper, some properties of strongly Harmonic ring are obtained by using some topological properties of the spectra [ Specl（R） ,Г^2（R）]. It is proved that if R any ring and N （R） is a prime radical of R, then R/N（R） is a strongly Harmonic ring if and only if [Specl（R）, Г^2（R） ] is a normal space. The relationships of clopen sets in [ Specl （R）, Г^2（R）] and idempotents in R are investigated.