Math 2.0

Algebraic geometry Concept

Basic open set

Summary

A basic open set of the spectrum of a commutative ring RR is a set D(f)D(f) of prime ideals not containing a fixed element ff. These sets form a basis of the Zariski topology. The set D(f)D(f) is in natural bijection with the spectrum of the localization RfR_f, so basic open sets are again spectra of rings.

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Further reading

  1. Web https://en.wikipedia.org/wiki/Spectrum_of_a_ring
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Changed2 November 2026

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