Theorems · Theorem · commutative algebra
Ideal.map_iInf_comap_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] {ι : Sort u_3},
Function.Surjective ⇑f → ∀ (K : ι → Ideal S), Ideal.map f (⨅ i, Ideal.comap f (K i)) = iInf K- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- FunLikestatement and proof · cited by 2,560
- iInfstatement · cited by 1,690
- Ideal.mapstatement · cited by 692
- Ideal.comapstatement · cited by 443
- RingHomClassstatement and proof · cited by 193
- GaloisInsertion.l_iInf_uproof · cited by 10
- Ideal.giMapComapproof · cited by 6
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