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Z is a Euclidean domain (#86)

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Patrick Stevens
2019-12-07 13:00:18 +00:00
committed by GitHub
parent cfd9787bb8
commit e192f0e1f1
38 changed files with 1018 additions and 486 deletions
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3
Rings/Ideals/Definition.agda
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@@ -25,6 +25,7 @@ open Equivalence eq
open Group additiveGroup
open import Rings.Lemmas R
open import Rings.Divisible.Definition R
record Ideal {c : _} (pred : A → Set c) : Set (a ⊔ b ⊔ c) where
field
@@ -37,7 +38,7 @@ record Ideal {c : _} (pred : A → Set c) : Set (a ⊔ b ⊔ c) where
predicate = pred
generatedIdealPred : A → A → Set (a ⊔ b)
generatedIdealPred a b = Sg A (λ c → Setoid._∼_ S (a * c) b)
generatedIdealPred a b = a ∣ b
generatedIdeal : (a : A) → Ideal (generatedIdealPred a)
Subgroup.isSubset (Ideal.isSubgroup (generatedIdeal a)) {x} {y} x=y (c , prC) = c , transitive prC x=y