Theorems · Theorem · commutative algebra
Ideal.quotientEquivAlg_mk
∀ {R₁ : Type u_1} {A : Type u_3} {B : Type u_4} [inst : CommSemiring R₁] [inst_1 : Ring A] [inst_2 : Algebra R₁ A]
[inst_3 : Ring B] [inst_4 : Algebra R₁ B] {I : Ideal A} (J : Ideal B) [inst_5 : I.IsTwoSided] [inst_6 : J.IsTwoSided]
(f : A ≃ₐ[R₁] B) (hIJ : J = Ideal.map (↑f) I) (x : A),
(I.quotientEquivAlg J f hIJ) ((Ideal.Quotient.mk I) x) = (Ideal.Quotient.mk J) (f x)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- AlgEquivstatement and proof · cited by 1,681
- RingHomClass.toRingHomstatement and proof · cited by 746
- Ideal.mapstatement and proof · cited by 692
- Ideal.Quotient.mkstatement · cited by 610
- Ideal.IsTwoSidedstatement and proof · cited by 179
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