mirror of
https://github.com/Smaug123/agdaproofs
synced 2025-10-11 14:48:42 +00:00
25 lines
886 B
Agda
25 lines
886 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
|
|
|
|
open import LogicalFormulae
|
|
open import Groups.Groups
|
|
open import Groups.Homomorphisms.Definition
|
|
open import Groups.Definition
|
|
open import Numbers.Naturals.Naturals
|
|
open import Setoids.Orders
|
|
open import Setoids.Setoids
|
|
open import Functions
|
|
open import Sets.EquivalenceRelations
|
|
open import Rings.Definition
|
|
open import Rings.Homomorphisms.Definition
|
|
open import Groups.Homomorphisms.Lemmas
|
|
|
|
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
|
|
|
|
module Rings.PrincipalIdealDomain {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} (R : Ring S _+_ _*_) where
|
|
|
|
open import Rings.Ideals.Principal.Definition R
|
|
open import Rings.Ideals.Definition R
|
|
|
|
PrincipalIdealDomain : {c : _} → Set (a ⊔ b ⊔ lsuc c)
|
|
PrincipalIdealDomain {c} = {pred : A → Set c} → (ideal : Ideal pred) → PrincipalIdeal ideal
|