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17 lines
629 B
Agda
17 lines
629 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import LogicalFormulae
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open import Setoids.Setoids
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open import Rings.Definition
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open import Rings.Ideals.Definition
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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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
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record PrimeIdeal : Set (a ⊔ c) where
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field
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isPrime : {a b : A} → pred (a * b) → ((pred a) → False) → pred b
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notContained : A
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notContainedIsNotContained : (pred notContained) → False
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