Theorems · Theorem · algebraic geometry
PrimeSpectrum.zeroLocus_eq_basicOpen_of_isIdempotentElem
∀ {R : Type u} [inst : CommRing R] (e : R),
IsIdempotentElem e → PrimeSpectrum.zeroLocus {e} = ↑(PrimeSpectrum.basicOpen (1 - e))[Stacks Tag 00EC](https://stacks.math.columbia.edu/tag/00EC)
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- SetLike.coestatement · cited by 8,199
- TopologicalSpace.Opensstatement · cited by 2,040
- PrimeSpectrumstatement and proof · cited by 625
- IsIdempotentElemstatement and proof · cited by 217
- PrimeSpectrum.zeroLocusstatement and proof · cited by 164
- PrimeSpectrum.basicOpenstatement · cited by 163
- sub_sub_cancelproof · cited by 105
- IsIdempotentElem.one_subproof · cited by 20
- PrimeSpectrum.basicOpen_eq_zeroLocus_of_isIdempotentElemproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.isClopen_iff_zeroLocusproof · cited by 1