Theorems · Definition · commutative algebra
RingCon.comapQuotientEquivRange
{M : Type u_1} →
{N : Type u_2} →
[inst : Ring M] →
[inst_1 : Ring N] →
(c : RingCon M) → (f : N →+* M) → {d : RingCon N} → d = c.comap f → d.Quotient ≃+* ↥(c.mk'.comp f).rangeThe second isomorphism theorem for rings.
- Defined in
- Mathlib.RingTheory.Congruence.Hom
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 38 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
- RingEquivstatement · cited by 1,147
- RingHom.compstatement · cited by 899
- Subringstatement · cited by 602
- RingConstatement and proof · cited by 219
- RingHom.rangestatement · cited by 138
- RingCon.Quotientstatement · cited by 118
- RingCon.comapstatement and proof · cited by 32
- RingCon.mk'statement · cited by 23
- RingCon.comapQuotientEquivRangeSproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- RingCon.comapQuotientEquivRange.congr_simpstatement and proof · cited by 0
- RingCon.comapQuotientEquivRange_mkstatement · cited by 0
- RingCon.comapQuotientEquivRange_symm_mkstatement and proof · cited by 0
- RingCon.coe_comapQuotientEquivRange_mkstatement · cited by 0