Английская Википедия:Constructible topology
In commutative algebra, the constructible topology on the spectrum <math>\operatorname{Spec}(A)</math> of a commutative ring <math>A</math> is a topology where each closed set is the image of <math>\operatorname{Spec} (B)</math> in <math>\operatorname{Spec}(A)</math> for some algebra B over A. An important feature of this construction is that the map <math>\operatorname{Spec}(B) \to \operatorname{Spec}(A)</math> is a closed map with respect to the constructible topology.
With respect to this topology, <math>\operatorname{Spec}(A)</math> is a compact,[1] Hausdorff, and totally disconnected topological space (i.e., a Stone space). In general, the constructible topology is a finer topology than the Zariski topology, and the two topologies coincide if and only if <math>A / \operatorname{nil}(A)</math> is a von Neumann regular ring, where <math>\operatorname{nil}(A)</math> is the nilradical of A.[2]
Despite the terminology being similar, the constructible topology is not the same as the set of all constructible sets.[3]
See also
References
Шаблон:Topology-stub
Шаблон:Commutative-algebra-stub
- ↑ Some authors prefer the term quasicompact here.
- ↑ Шаблон:Cite web
- ↑ Шаблон:Cite web