论文标题
$ S $ -FLAT拓扑
The $S$-flat topology
论文作者
论文摘要
对于$ 1 \ ne 0 $的通勤环$ r $和$ r $ $ r $的多个封闭的子集$ s $，我们在$ s $ s $ prime spectrum $ \ mathrm {spec} _sr of $ r $的$ s $ r $上引入了新的拓扑，称为$ s $ s $ flat topology。我们的目的是对这种新拓扑的拓扑特性进行代数描述，例如紧凑，不可约性，连通性和Noetherianess。
For a commutative ring $R$ with unit $1\ne 0$ and a multiplicatively closed subset $S$ of $R$, we introduce a new topology on the $S$-prime spectrum $\mathrm{Spec}_SR$ of $R$ called the $S$-flat topology. Our aims is to give an algebraic descriptions of the topological properties like compactness, irreducibility, connectivity and noetherianess with respect to this new topology .
