Theorems · Theorem · commutative algebra
ValuationSubring.le_ofPrime
∀ {K : Type u} [inst : Field K] (A : ValuationSubring K) (P : Ideal ↥A) [inst_1 : P.IsPrime], A ≤ A.ofPrime P- Cited by
- 2 results in Mathlib
- Foundations
- Depth 67 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Idealstatement and proof · cited by 4,748
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.primeComplproof · cited by 462
- ValuationSubringstatement and proof · cited by 187
- Subalgebra.algebraMap_memproof · cited by 28
- ValuationSubring.ofPrimestatement · cited by 10
- Localization.subalgebra.ofFieldproof · cited by 8
- Subalgebra.mem_toSubringproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- ValuationSubring.ofPrime_idealOfLEproof · cited by 2
- ValuationSubring.idealOfLE_ofPrimestatement · cited by 0