Theorems · Theorem · algebraic geometry
PrimeSpectrum.zeroLocus_empty
∀ {R : Type u} [inst : CommSemiring R], PrimeSpectrum.zeroLocus ∅ = Set.univ- Defined in
- Mathlib.RingTheory.Spectrum.Prime.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- Set.univstatement · cited by 3,945
- PrimeSpectrumstatement · cited by 625
- PrimeSpectrum.zeroLocusstatement · cited by 164
- GaloisConnection.l_botproof · cited by 63
- PrimeSpectrum.gc_setproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.mem_image_comap_basicOpenproof · cited by 3