Theorems · Theorem · commutative algebra
Ideal.comap_map_quotientMk
∀ {R : Type u} [inst : Ring R] (I J : Ideal R) [inst_1 : I.IsTwoSided],
Ideal.comap (Ideal.Quotient.mk I) (Ideal.map (Ideal.Quotient.mk I) J) = I ⊔ J- Cited by
- 5 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingIdeal.IsTwoSided
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- Ideal.mapstatement · cited by 692
- Ideal.Quotient.mkstatement · cited by 610
- Ideal.comapstatement · cited by 443
- Ideal.IsTwoSidedstatement and proof · cited by 179
- sup_commproof · cited by 165
- Ideal.extproof · cited by 131
Cited by5
Results whose statement or proof uses this declaration.
- Ideal.comap_map_mkproof · cited by 2
- Ideal.map_sup_mem_minimalPrimes_of_map_quotientMk_mem_minimalPrimesproof · cited by 1
- Ideal.height_eq_height_add_of_liesOver_of_hasGoingDownproof · cited by 1
- Ideal.mem_minimalPrimes_supproof · cited by 1
- Algebra.WeaklyQuasiFiniteAt.eq_of_le_of_under_eqproof · cited by 0