Lots of rings (#82)

Rings/Ideals/Prime/Definition.agda

@@ -0,0 +1,22 @@
+{-# OPTIONS --safe --warning=error --without-K #-}
+
+open import LogicalFormulae
+open import Groups.Groups
+open import Groups.Lemmas
+open import Groups.Definition
+open import Numbers.Naturals.Naturals
+open import Orders
+open import Setoids.Setoids
+open import Functions
+open import Rings.Definition
+open import Rings.Lemmas
+open import Sets.EquivalenceRelations
+open import Fields.Fields
+open import Rings.Ideals.Definition
+
+open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
+
+module Rings.Ideals.Prime.Definition {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} {R : Ring S _+_ _*_} {c : _} {pred : A → Set c} (i : Ideal R pred) where
+
+PrimeIdeal : Set (a ⊔ c)
+PrimeIdeal = {a b : A} → pred (a * b) → ((pred a) → False) → pred b