Theorems · Theorem · commutative algebra
Ideal.Quotient.factor_ker
∀ {R : Type u_1} [inst : Ring R] {I J : Ideal R} (H : I ≤ J) [inst_1 : I.IsTwoSided] [inst_2 : J.IsTwoSided],
RingHom.ker (Ideal.Quotient.factor H) = Ideal.map (Ideal.Quotient.mk I) J- Cited by
- 3 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHomstatement · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Ideal.mapstatement and proof · cited by 692
- Ideal.Quotient.mkstatement and proof · cited by 610
- RingHom.kerstatement and proof · cited by 363
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Ideal.Quotient.mk_surjectiveproof · cited by 134
- Ideal.extproof · cited by 131
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.map_mk_comap_factorproof · cited by 1
- AdicCompletion.ker_evalOneₐ_eq_mapproof · cited by 1
- factorPowSucc.isUnit_of_isUnit_imageproof · cited by 0