Theorems · Definition · commutative algebra
DoubleQuot.quotQuotToQuotSup
{R : Type u} → [inst : CommRing R] → (I J : Ideal R) → (R ⧸ I) ⧸ Ideal.map (Ideal.Quotient.mk I) J →+* R ⧸ I ⊔ JThe ring homomorphism (R/I)/J' -> R/(I ⊔ J) induced by quotLeftToQuotSup where J'
is the image of J in R/I
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- Ideal.mapstatement and proof · cited by 692
- Ideal.Quotient.mkstatement and proof · cited by 610
- Ideal.Quotient.liftproof · cited by 19
- DoubleQuot.quotLeftToQuotSupproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- DoubleQuot.quotQuotEquivQuotSupproof · cited by 9
- DoubleQuot.quotQuotToQuotSupₐproof · cited by 2
- DoubleQuot.coe_quotQuotToQuotSupₐstatement · cited by 0
- DoubleQuot.quotQuotToQuotSupₐ_toRingHomstatement · cited by 0