Theorems · Definition · commutative algebra
RingCon.comapQuotientEquivRangeS
{M : Type u_1} →
{N : Type u_2} →
[inst : NonAssocSemiring M] →
[inst_1 : NonAssocSemiring N] →
(c : RingCon M) → (f : N →+* M) → {d : RingCon N} → d = c.comap f → d.Quotient ≃+* ↥(c.mk'.comp f).rangeSThe second isomorphism theorem for semirings.
- Defined in
- Mathlib.RingTheory.Congruence.Hom
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- RingEquivstatement · cited by 1,147
- RingHom.compstatement and proof · cited by 899
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement · cited by 456
- RingConstatement and proof · cited by 219
- RingCon.Quotientstatement · cited by 118
- RingEquiv.reflproof · cited by 72
- RingEquiv.transproof · cited by 54
- RingHom.rangeSstatement · cited by 47
- RingCon.comapstatement and proof · cited by 32
- RingCon.mk'statement and proof · cited by 23
Cited by4
Results whose statement or proof uses this declaration.
- RingCon.comapQuotientEquivRangeproof · cited by 4
- RingCon.comapQuotientEquivRangeS.congr_simpstatement and proof · cited by 0
- RingCon.comapQuotientEquivRangeS_mkstatement · cited by 0
- RingCon.comapQuotientEquivRangeS_symm_mkstatement and proof · cited by 0