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Cubical/Algebra/CommAlgebra/FGIdeal.agda
@@ -45,6 +45,10 @@ module _ (A : CommAlgebra R ℓ') where
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→ (∀ i → V i ∈ fst I) → fst ⟨ V ⟩[ A ] ⊆ fst I
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inclOfFGIdeal V I ∀i→Vi∈I = CommRing.inclOfFGIdeal (CommAlgebra→CommRing A) V I ∀i→Vi∈I
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+{-
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+ The image of an fg ideal under a surjection is an fg ideal generated by the
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+ images of the generators
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+-}
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imageIdealIsImageFGIdeal :
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{n : ℕ} (A : CommAlgebra R ℓ') (g : FinVec ⟨ A ⟩ₐ n) (B : CommAlgebra R ℓ')
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(f : CommAlgebraHom A B) (surjective : isSurjection ⟨ f ⟩ₐ→)
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