Theorems · Theorem · commutative algebra
IsLocalization.AtPrime.equivQuotMaximalIdeal_symm_apply_mk
∀ {R : Type u_7} [inst : CommRing R] (p : Ideal R) [inst_1 : p.IsMaximal] (Rₚ : Type u_8) [inst_2 : CommRing Rₚ]
[inst_3 : Algebra R Rₚ] [inst_4 : IsLocalization.AtPrime Rₚ p] [inst_5 : IsLocalRing Rₚ] (x : R) (s : ↥p.primeCompl),
(IsLocalization.AtPrime.equivQuotMaximalIdeal p Rₚ).symm
((Ideal.Quotient.mk (IsLocalRing.maximalIdeal Rₚ)) (IsLocalization.mk' Rₚ x s)) =
(Ideal.Quotient.mk p) x * ((Ideal.Quotient.mk p) ↑s)⁻¹- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites32
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
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- Submonoidstatement · cited by 3,086
- HasQuotient.Quotientstatement and proof · cited by 2,301
- mul_assocproof · cited by 1,667
- RingEquivstatement · cited by 1,147
- map_mulproof · cited by 1,137
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalization.AtPrime.algebraMap_equivQuotMaximalIdeal_symm_applyproof · cited by 1