Übersetzung für 'Zariski topology' von Englisch nach Deutsch

Zariski topology

Zariski-Topologie {f}math.

• 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 [...].

  ---