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Lots of rings (#82)

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Patrick Stevens
2019-11-22 19:52:57 +00:00
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parent b33baa5fb7
commit 660d7aa27c
40 changed files with 1246 additions and 881 deletions
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Rings/Ideals/Principal/Definition.agda Normal file
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{-# 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.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 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))