Theorems · Theorem · commutative algebra
Ideal.Quotient.mk_algebraMap
∀ (R₁ : Type u_1) {A : Type u_3} [inst : CommSemiring R₁] [inst_1 : Ring A] [inst_2 : Algebra R₁ A] (I : Ideal A)
[inst_3 : I.IsTwoSided] (x : R₁), (Ideal.Quotient.mk I) ((algebraMap R₁ A) x) = (algebraMap R₁ (A ⧸ I)) x- Cited by
- 4 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Algebra.algebraMapstatement · cited by 4,706
- HasQuotient.Quotientstatement · cited by 2,301
- Ideal.Quotient.mkstatement · cited by 610
- Ideal.IsTwoSidedstatement and proof · cited by 179
Cited by4
Results whose statement or proof uses this declaration.
- IsLocalization.AtPrime.equivQuotMaximalIdeal_symm_apply_mkproof · cited by 1
- IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_symm_apply_mkproof · cited by 1
- liftOfDerivationToSquareZero_mk_applyproof · cited by 0
- Ideal.comap_eq_of_scalar_tower_quotientproof · cited by 0