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Polynomial ring (#76)

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Patrick Stevens
2019-11-17 17:37:10 +00:00
committed by GitHub
parent c55dd5f63e
commit 8377c23613
23 changed files with 984 additions and 341 deletions
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Rings/Ideals/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 Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Rings.Ideals.Definition {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} (R : Ring S _+_ _*_) where
ringKernel : {c d : _} {C : Set c} {T : Setoid {c} {d} C} {_+2_ _*2_ : C → C → C} (R2 : Ring T _+2_ _*2_) {f : A → C} (fHom : RingHom R R2 f) → Set (a ⊔ d)
ringKernel {T = T} R2 {f} fHom = Sg A (λ a → Setoid._∼_ T (f a) (Ring.0R R2))