Theorems · Theorem · algebraic geometry
PrimeSpectrum.isClopen_basicOpen_of_mul_add
∀ {R : Type u} [inst : CommSemiring R] (e f : R), e * f = 0 → e + f = 1 → IsClopen ↑(PrimeSpectrum.basicOpen e)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement · cited by 8,199
- TopologicalSpace.Opensstatement · cited by 2,040
- PrimeSpectrumstatement · cited by 625
- IsClopenstatement · cited by 189
- PrimeSpectrum.basicOpenstatement and proof · cited by 163
- TopologicalSpace.Opens.is_open'proof · cited by 139
- PrimeSpectrum.isClosed_zeroLocusproof · cited by 10
- PrimeSpectrum.basicOpen_eq_zeroLocus_of_mul_addproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.isClopen_iff_mul_addproof · cited by 1