Theorems · Theorem · commutative algebra
LocalSubring.le_ofPrime
∀ {K : Type u_3} [inst : Field K] (A : Subring K) (P : Ideal ↥A) [inst_1 : P.IsPrime],
A ≤ (LocalSubring.ofPrime A P).toSubring- Cited by
- 3 results in Mathlib
- Foundations
- Depth 66 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- Ideal.IsPrimestatement and proof · cited by 827
- Subringstatement and proof · cited by 602
- Localization.AtPrimeproof · cited by 299
- LocalSubring.toSubringstatement · cited by 18
- IsLocalization.lift_eqproof · cited by 14
- LocalSubring.ofPrimestatement · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.image_subset_nonunits_valuationSubringproof · cited by 2
- LocalSubring.map_maximalIdeal_eq_top_of_isMaxproof · cited by 1
- LocalSubring.mem_of_isMax_of_isIntegralproof · cited by 1