Theorems · Theorem · commutative algebra
Ideal.Quotient.factor_eq
∀ {R : Type u} [inst : Ring R] {S : Ideal R} [inst_1 : S.IsTwoSided], Ideal.Quotient.factor ⋯ = RingHom.id (R ⧸ S)- Defined in
- Mathlib.RingTheory.Ideal.Quotient.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingIdeal.IsTwoSided
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- 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
- le_reflstatement · cited by 2,061
- Ideal.Quotient.mkproof · cited by 610
- RingHom.extproof · cited by 331
- Ideal.IsTwoSidedstatement and proof · cited by 179
- RingHomCompTriple.comp_eqproof · cited by 38
- Ideal.Quotient.factorstatement · cited by 33
Cited by5
Results whose statement or proof uses this declaration.
- AdicCompletion.evalₐ_liftRingHomproof · cited by 4
- Algebra.FormallySmooth.exists_adicCompletionEvalOneₐ_comp_eqproof · cited by 2
- AdicCompletion.factor_eval_liftRingHomproof · cited by 0
- AdicCompletion.factor_evalₐ_eq_evalproof · cited by 0
- Ideal.Quotient.factorₐ_reflproof · cited by 0