Theorems · Theorem · commutative algebra
MaximalSpectrum.toPiLocalization_not_surjective_of_infinite
∀ {ι : Type u_5} (R : ι → Type u_4) [inst : (i : ι) → CommSemiring (R i)] [∀ (i : ι), Nontrivial (R i)] [Infinite ι],
¬Function.Surjective ⇑(MaximalSpectrum.toPiLocalization ((i : ι) → R i))- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Idealproof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- Set.rangeproof · cited by 4,705
- AlgHomstatement · cited by 3,236
- Nontrivialstatement and proof · cited by 2,416
- map_zeroproof · cited by 1,614
- Function.updateproof · cited by 502
- Ideal.primeComplstatement · cited by 462
- Ideal.IsMaximalproof · cited by 452
- Ideal.comapproof · cited by 443
Cited by2
Results whose statement or proof uses this declaration.
- MaximalSpectrum.finite_of_toPiLocalization_pi_surjectiveproof · cited by 1
- PrimeSpectrum.toPiLocalization_not_surjective_of_infiniteproof · cited by 1