Theorems · Theorem · commutative algebra
Algebra.Smooth.of_isLocalization_Away
∀ {R : Type u_4} [inst : CommRing R] {A : Type u_5} [inst_1 : CommRing A] [inst_2 : Algebra R A] (r : R)
[IsLocalization.Away r A], Algebra.Smooth R ALocalization at an element is smooth.
- Defined in
- Mathlib.RingTheory.Smooth.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 131 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.Smoothstatement · cited by 22
- IsLocalization.Away.finitePresentationproof · cited by 7
- Algebra.FormallySmooth.of_isLocalizationproof · cited by 6
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