Theorems · Theorem · commutative algebra
Ideal.comap_le_comap_iff_of_surjective
∀ {R : Type u} {S : Type v} {F : Type u_1} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : FunLike F R S] (f : F)
[inst_3 : RingHomClass F R S], Function.Surjective ⇑f → ∀ (I J : Ideal S), Ideal.comap f I ≤ Ideal.comap f J ↔ I ≤ J- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, 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.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- LE.le.transproof · cited by 3,151
- FunLikestatement and proof · cited by 2,560
- Eq.leproof · cited by 605
- Ideal.comapstatement and proof · cited by 443
- RingHomClassstatement and proof · cited by 193
- Ideal.map_comap_of_surjectiveproof · cited by 13
- Ideal.map_le_of_le_comapproof · cited by 6
- Ideal.le_comap_of_map_leproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.orderEmbeddingOfSurjectiveproof · cited by 6