Theorems · Definition · commutative algebra
Localization.awayEquivAdjoin
{R : Type u_1} →
[inst : CommRing R] → (r : R) → Localization.Away r ≃ₐ[R] AdjoinRoot (Polynomial.C r * Polynomial.X - 1)The R-AlgEquiv between the localization of R away from r and
R with an inverse of r adjoined.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement · cited by 5,681
- AlgEquivstatement · cited by 1,681
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Submonoid.powersstatement · cited by 408
- AdjoinRootstatement and proof · cited by 177
- Algebra.ofIdproof · cited by 166
- Localization.Awaystatement and proof · cited by 162
- AdjoinRoot.ofproof · cited by 52
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalization.Away.finitePresentationproof · cited by 7
- IsLocalization.adjoin_invproof · cited by 0