Theorems · Theorem · commutative algebra
Ideal.map_iSup
∀ {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)
[RingHomClass F R S] {ι : Sort u_3} (K : ι → Ideal R), Ideal.map f (iSup K) = ⨆ i, Ideal.map f (K i)- 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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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- FunLikestatement and proof · cited by 2,560
- iSupstatement · cited by 2,415
- Ideal.mapstatement · cited by 692
- RingHomClassstatement and proof · cited by 193
- GaloisConnection.l_iSupproof · cited by 78
- Ideal.gc_map_comapproof · cited by 17
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