Constructible topology

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In commutative algebra, the constructible topology on the spectrum of a commutative ring is a topology where each closed set is the image of in for some algebra B over A. An important feature of this construction is that the map is a closed map with respect to the constructible topology.

With respect to this topology, is a compact,[1] Hausdorff, and totally disconnected topological space. In general the constructible topology is a finer topology than the Zariski topology, but the two topologies will coincide if and only if is a von Neumann regular ring, where is the nilradical of A.

See also

References

  1. Some authors prefer the term quasicompact here.
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