Theorems · Definition · commutative algebra
RingCon.quotientQuotientEquivQuotient
{M : Type u_1} →
[inst : NonAssocSemiring M] → (c d : RingCon M) → (h : c ≤ d) → (RingCon.ker (c.map d h)).Quotient ≃+* d.QuotientThe third isomorphism theorem for (semi-)rings.
- Defined in
- Mathlib.RingTheory.Congruence.Hom
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Quot.sound
- Assumes
- NonAssocSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivproof · cited by 8,337
- RingEquivstatement · cited by 1,147
- NonAssocSemiringstatement and proof · cited by 805
- RingConstatement and proof · cited by 219
- RingCon.Quotientstatement · cited by 118
- RingCon.kerstatement · cited by 47
- Setoid.kerproof · cited by 43
- Con.toSetoidproof · cited by 38
- RingCon.toConproof · cited by 36
- RingCon.mapstatement · cited by 4
- Setoid.quotientQuotientEquivQuotientproof · cited by 0
- Quot.mapRightproof · cited by 0
Cited by4
Results whose statement or proof uses this declaration.
- RingCon.quotientQuotientEquivQuotientₐproof · cited by 3
- RingCon.quotientQuotientEquivQuotient_coe_coestatement · cited by 0
- RingCon.quotientQuotientEquivQuotient_mk_mkstatement · cited by 0
- RingCon.quotientQuotientEquivQuotient_symm_mkstatement · cited by 0