Theorems · Theorem · algebraic geometry
PrimeSpectrum.basicOpen_injOn_isIdempotentElem
∀ {R : Type u} [inst : CommSemiring R], Set.InjOn PrimeSpectrum.basicOpen {e | IsIdempotentElem e}- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 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.
Cites16
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
- Set.ofPredstatement and proof · cited by 6,101
- Idealproof · cited by 4,748
- mul_commproof · cited by 2,262
- TopologicalSpace.Opensstatement · cited by 2,040
- mul_assocproof · cited by 1,667
- Ideal.spanproof · cited by 948
- Ideal.IsPrimeproof · cited by 827
- PrimeSpectrumstatement · cited by 625
- Set.InjOnstatement · cited by 543
- IsIdempotentElemstatement and proof · cited by 217
- PrimeSpectrum.basicOpenstatement and proof · cited by 163
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.existsUnique_idempotent_basicOpen_eq_of_isClopenproof · cited by 0