Theorems · Theorem · commutative algebra
Ideal.Quotient.ringHom_ext
∀ {R : Type u} [inst : Ring R] {I : Ideal R} {S : Type v} [inst_1 : I.IsTwoSided] [inst_2 : NonAssocSemiring S]
⦃f g : R ⧸ I →+* S⦄, f.comp (Ideal.Quotient.mk I) = g.comp (Ideal.Quotient.mk I) → f = gTwo RingHoms from the quotient by an ideal are equal if their
compositions with Ideal.Quotient.mk' are equal.
See note [partially-applied ext lemmas].
- Defined in
- Mathlib.RingTheory.Ideal.Quotient.Defs
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 83 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.
- 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
- RingHom.compstatement and proof · cited by 899
- NonAssocSemiringstatement and proof · cited by 805
- Ideal.Quotient.mkstatement and proof · cited by 610
- RingHom.extproof · cited by 331
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Quotient.inductionOn'proof · cited by 69
- RingHom.congr_funproof · cited by 29
Cited by17
Results whose statement or proof uses this declaration.
- Ideal.Quotient.factor_eqproof · cited by 5
- Ring.DirectLimit.hom_extproof · cited by 5
- IsLocalRing.ResidueField.map_compproof · cited by 3
- IsLocalRing.ResidueField.map_idproof · cited by 3
- AdjoinRoot.ringHom_extproof · cited by 3
- Ideal.ResidueField.ringHom_extproof · cited by 3
- NumberField.InfinitePlace.inertiaDeg_eq_finrankproof · cited by 2
- Ideal.card_stabilizer_eq_card_inertia_mul_finrankproof · cited by 2
- Ideal.Quotient.factor_compproof · cited by 1
- IsLocalization.AtPrime.inertiaDeg_map_eq_inertiaDegproof · cited by 1
- trace_quotient_eq_trace_localization_quotientproof · cited by 1