Theorems · Theorem · commutative algebra
Localization.subalgebra.ofField_eq
∀ {A : Type u_1} (K : Type u_2) [inst : CommRing A] (S : Submonoid A) (hS : S ≤ nonZeroDivisors A) [inst_1 : Field K]
[inst_2 : Algebra A K] [inst_3 : IsFractionRing A K],
Localization.subalgebra.ofField K S hS = Localization.subalgebra K S hS- Cited by
- 1 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Set.ofPredproof · cited by 6,101
- Algebra.algebraMapproof · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- Subalgebrastatement · cited by 1,353
- nonZeroDivisorsstatement and proof · cited by 895
- IsFractionRingstatement and proof · cited by 738
- Localizationproof · cited by 270
- IsLocalization.mk'proof · cited by 218
Cited by1
Results whose statement or proof uses this declaration.
- IsIntegrallyClosed.of_localization_maximalproof · cited by 2