Theorems · Theorem · commutative algebra
PrimeSpectrum.isMaximal_of_toPiLocalization_surjective
∀ {R : Type u_1} [inst : CommSemiring R],
Function.Surjective ⇑(PrimeSpectrum.toPiLocalization R) → ∀ (I : PrimeSpectrum R), I.asIdeal.IsMaximal- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 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.
Cites25
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
- SetLike.coeproof · cited by 8,199
- Idealproof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement · cited by 3,236
- IsUnitproof · cited by 1,602
- one_ne_zeroproof · cited by 885
- map_oneproof · cited by 861
- PrimeSpectrumstatement and proof · cited by 625
- Function.updateproof · cited by 502
- Ideal.primeComplstatement and proof · cited by 462
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.discreteTopology_of_toLocalization_surjectiveproof · cited by 1