Theorems · Theorem · commutative algebra
Algebra.Etale.of_isLocalizationAway
∀ {R : Type u} {A : Type v} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] (r : R)
[IsLocalization.Away r A], Algebra.Etale R ALocalization at an element is étale.
- Defined in
- Mathlib.RingTheory.Etale.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Submonoid.powersproof · cited by 408
- IsLocalization.Awaystatement and proof · cited by 218
- Algebra.Etalestatement · cited by 34
- IsLocalization.Away.finitePresentationproof · cited by 7
- Algebra.FormallyEtale.of_isLocalizationproof · cited by 3
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