Theorems · Theorem · algebraic geometry
PrimeSpectrum.basicOpen_mul
∀ {R : Type u} [inst : CommSemiring R] (f g : R),
PrimeSpectrum.basicOpen (f * g) = PrimeSpectrum.basicOpen f ⊓ PrimeSpectrum.basicOpen g- Cited by
- 5 results in Mathlib
- Foundations
- Depth 81 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.
Cites10
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
- Compl.complproof · cited by 2,925
- TopologicalSpace.Opensstatement · cited by 2,040
- PrimeSpectrumstatement · cited by 625
- PrimeSpectrum.zeroLocusproof · cited by 164
- PrimeSpectrum.basicOpenstatement · cited by 163
- TopologicalSpace.Opens.extproof · cited by 83
- PrimeSpectrum.basicOpen_eq_zeroLocus_complproof · cited by 34
- Set.compl_unionproof · cited by 30
- PrimeSpectrum.zeroLocus_singleton_mulproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- PrimeSpectrum.toPiLocalization_surjective_of_discreteTopologyproof · cited by 2
- AlgebraicGeometry.Proj.homOfLE_toBasicOpenOfGlobalSections_ιproof · cited by 1
- PrimeSpectrum.basicOpen_mul_le_leftproof · cited by 1
- PrimeSpectrum.basicOpen_mul_le_rightproof · cited by 0
- AlgebraicGeometry.StructureSheaf.exists_constproof · cited by 0