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Irreducible and maximal (#87)

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Patrick Stevens
2019-12-07 18:53:08 +00:00
committed by GitHub
parent e192f0e1f1
commit 99c38495ce
9 changed files with 123 additions and 19 deletions
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8
Rings/Ideals/Principal/Definition.agda
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@@ -18,7 +18,11 @@ open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Rings.Ideals.Principal.Definition {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} (R : Ring S _+_ _*_) where
open import Rings.Ideals.Definition R
open import Rings.Divisible.Definition R
open Setoid S
PrincipalIdeal : {c : _} {pred : A → Set c} (ideal : Ideal pred) → Set (a ⊔ b ⊔ c)
PrincipalIdeal {pred = pred} ideal = Sg A (λ a → {x : A} → (pred x) → Sg A (λ c → (a * c) ∼ x))
record PrincipalIdeal {c : _} {pred : A → Set c} (ideal : Ideal pred) : Set (a ⊔ b ⊔ c) where
field
generator : A
genIsInIdeal : pred generator
genGenerates : {x : A} → pred x → generator ∣ x