Theorems · Theorem · commutative algebra
Ideal.quotientMap_surjective
∀ {R : Type u} [inst : Ring R] {S : Type v} [inst_1 : Ring S] {J : Ideal R} {I : Ideal S} [inst_2 : I.IsTwoSided]
[inst_3 : J.IsTwoSided] {f : R →+* S} {H : J ≤ Ideal.comap f I},
Function.Surjective ⇑f → Function.Surjective ⇑(Ideal.quotientMap I f H)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- RingHomstatement and proof · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Ideal.Quotient.mkproof · cited by 610
- Ideal.comapstatement and proof · cited by 443
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Ideal.Quotient.mk_surjectiveproof · cited by 134
- Ideal.quotientMapstatement and proof · cited by 27
- Ideal.quotientMap_mkproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.WeaklyQuasiFiniteAt.of_algHom_localizationproof · cited by 1
- Algebra.WeaklyQuasiFiniteAt.of_restrictScalarsproof · cited by 1