Theorems · Theorem · commutative algebra
Ideal.Quotient.lift_mk
∀ {R : Type u} [inst : Ring R] (I : Ideal R) {a : R} {S : Type v} [inst_1 : I.IsTwoSided] [inst_2 : Semiring S]
(f : R →+* S) (H : ∀ a ∈ I, f a = 0), (Ideal.Quotient.lift I f H) ((Ideal.Quotient.mk I) a) = f a- Defined in
- Mathlib.RingTheory.Ideal.Quotient.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingIdeal.IsTwoSidedSemiring
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 and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- 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
- Ideal.Quotient.mkstatement · cited by 610
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Ideal.Quotient.liftstatement · cited by 19
Cited by9
Results whose statement or proof uses this declaration.
- Ideal.quotientMap_mkproof · cited by 9
- AdjoinRoot.lift_mkproof · cited by 6
- Ideal.ker_quotient_liftproof · cited by 4
- RingHom.kerLift_mkproof · cited by 4
- RingHom.lift_injective_of_ker_le_idealproof · cited by 2
- Algebra.FinitePresentation.of_span_eq_top_targetproof · cited by 2
- Ideal.Quotient.liftₐ_compproof · cited by 1
- MvPolynomial.quotientEquivQuotientMvPolynomial_leftInverseproof · cited by 0
- Ideal.quotientMap_algebraMapproof · cited by 0