Theorems · Theorem · commutative algebra
Ideal.Quotient.factor_surjective
∀ {R : Type u} [inst : Ring R] {S T : Ideal R} [inst_1 : S.IsTwoSided] [inst_2 : T.IsTwoSided] (H : S ≤ T),
Function.Surjective ⇑(Ideal.Quotient.factor H)- Defined in
- Mathlib.RingTheory.Ideal.Quotient.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Ideal.Quotient.mk_surjectiveproof · cited by 134
- Ideal.Quotient.factorstatement · cited by 33
- Ideal.Quotient.lift_surjective_of_surjectiveproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- AdicCompletion.evalOneₐ_surjectiveproof · cited by 2
- IsLocalRing.finite_quotient_iffproof · cited by 0
- factorPowSucc.isUnit_of_isUnit_imageproof · cited by 0
- Module.finite_of_surjective_of_ker_le_nilradicalproof · cited by 0