|NOUN || Zariski topology | - |
NOUN article.ind sg | pl
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weitere Beispiele ...
- In contrast, non-preregular spaces are encountered much more frequently in abstract algebra and algebraic geometry, in particular as the Zariski topology on an algebraic variety or the spectrum of a ring.
- is often equipped with a Zariski topology. Again we also by convention require this locally ringed space to be irreducible.
- The étale topology is finer than the Zariski topology.
- The Zariski topology on the spectrum of a ring has a base consisting of open sets that have specific useful properties.
- It follows readily from the definition of the spectrum of a ring Spec("R"), the space of prime ideals of "R" equipped with the Zariski topology, that the Krull dimension of "R" is equal to the dimension of its spectrum as a topological space, meaning the supremum of the lengths of all chains of irreducible closed subsets.
- This topology is called the Zariski topology.
- This is finer than the Zariski topology.
- As another example, an algebraic subset "W" in "K'n" is irreducible (in the Zariski topology) if and only if [...] is a prime ideal.
- Since the Zariski topology on an algebraic variety or scheme "X" is much coarser than, say, the topology of open subsets in [...] it is no longer meaningful to consider continuous maps from an interval to "X".
- The closure on [...] is the closure in the Zariski topology, and if the field [...] is algebraically closed, then the closure on the polynomial ring is the radical of ideal generated by [...].
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