Theorems · Theorem · commutative algebra
Ideal.quotientMap_injective
∀ {R : Type u} [inst : Ring R] {S : Type v} [inst_1 : Ring S] {I : Ideal S} {f : R →+* S} [inst_2 : I.IsTwoSided],
Function.Injective ⇑(Ideal.quotientMap I f ⋯)If we take J = I.comap f then quotientMap is injective automatically.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingRingIdeal.IsTwoSided
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
- RingHomstatement and proof · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- le_rflstatement and proof · cited by 1,558
- Ideal.comapstatement · cited by 443
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Ideal.quotientMapstatement · cited by 27
- Ideal.quotientMap_injective'proof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.jacobson_bot_of_integral_localizationproof · cited by 0
- Polynomial.isMaximal_comap_C_of_isMaximalproof · cited by 0