Theorems · Theorem · commutative algebra
Ideal.algebraMap_quotient_injective
∀ {A : Type u_3} [inst : Ring A] {R : Type u_5} [inst_1 : CommRing R] {I : Ideal A} [inst_2 : I.IsTwoSided]
[inst_3 : Algebra R A], Function.Injective ⇑(algebraMap (R ⧸ Ideal.comap (algebraMap R A) I) (A ⧸ I))- Cited by
- 5 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- HasQuotient.Quotientstatement and proof · cited by 2,301
- map_subproof · cited by 565
- Ideal.comapstatement and proof · cited by 443
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Ideal.Quotient.eqproof · cited by 22
Cited by5
Results whose statement or proof uses this declaration.
- Ideal.isMaximal_comap_of_isIntegral_of_isMaximalproof · cited by 3
- Ideal.exists_ideal_over_prime_of_isIntegral_of_isPrimeproof · cited by 2
- IsArithFrobAt.exists_of_isInvariantproof · cited by 1
- isJacobsonRing_of_isIntegralproof · cited by 1
- Algebra.ker_algebraMap_isMaximal_of_isIntegralproof · cited by 0