Theorems · Theorem · commutative algebra
ValuationSubring.ofPrime_valuation_eq_one_iff_mem_primeCompl
∀ {K : Type u} [inst : Field K] (A : ValuationSubring K) (P : Ideal ↥A) [inst_1 : P.IsPrime] (x : ↥A),
(A.ofPrime P).valuation ↑x = 1 ↔ x ∈ P.primeCompl- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldIdeal.IsPrime
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Fieldstatement and proof · cited by 7,404
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- Submonoidstatement · cited by 3,086
- Ideal.IsPrimestatement and proof · cited by 827
- Valuationstatement · cited by 823
- Ideal.primeComplstatement · cited by 462
- ValuationSubringstatement and proof · cited by 187
- ValuationSubring.valuationstatement and proof · cited by 29
- ValuationSubring.ValueGroupstatement · cited by 26
- ValuationSubring.ofPrimestatement and proof · cited by 10
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.