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7 files changed

+20
-16
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src/Algebra/Construct/Quotient/Ring/Properties/ChineseRemainderTheorem.agda

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------------------------------------------------------------------------
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-- The Chinese Remainder Theorem for arbitrary rings
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--
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-- The Agda standard library
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--
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-- The Chinese Remainder Theorem for arbitrary rings
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------------------------------------------------------------------------
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{-# OPTIONS --safe --cubical-compatible #-}

src/Algebra/Ideal.agda

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------------------------------------------------------------------------
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-- Ideals of a ring
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--
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-- The Agda standard library
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--
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-- Ideals of a ring
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------------------------------------------------------------------------
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{-# OPTIONS --safe --cubical-compatible #-}

src/Algebra/Ideal/Construct/Intersection.agda

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------------------------------------------------------------------------
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-- Intersection of ideals
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--
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-- The Agda standard library
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--
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-- Intersection of ideals
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------------------------------------------------------------------------
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{-# OPTIONS --safe --cubical-compatible #-}

src/Algebra/Ideal/Construct/Kernel.agda

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{-# OPTIONS --safe --without-K #-}
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------------------------------------------------------------------------
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-- The Agda standard library
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--
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-- The kernel of a ring homomorphism is an ideal
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------------------------------------------------------------------------
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{-# OPTIONS --safe --cubical-compatible #-}
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open import Algebra.Bundles
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open import Algebra.Morphism.Structures

src/Algebra/Ideal/Coprimality.agda

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------------------------------------------------------------------------
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-- Coprimality of ideals
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--
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-- The Agda standard library
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--
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-- Coprimality of ideals
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------------------------------------------------------------------------
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{-# OPTIONS --safe --cubical-compatible #-}

src/Algebra/NormalSubgroup/Construct/Intersection.agda

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------------------------------------------------------------------------
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-- Intersection of normal subgroups
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--
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-- The Agda standard library
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--
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-- Intersection of normal subgroups
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------------------------------------------------------------------------
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{-# OPTIONS --safe --cubical-compatible #-}
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where
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module N = NormalSubgroup N
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module M = NormalSubgroup M
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src/Algebra/NormalSubgroup/Construct/Kernel.agda

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------------------------------------------------------------------------
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-- The kernel of a group homomorphism is a normal subgroup
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--
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-- The Agda standard library
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--
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-- The kernel of a group homomorphism is a normal subgroup
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------------------------------------------------------------------------
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{-# OPTIONS --safe --cubical-compatible #-}
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{ element = G.ε
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; inKernel = ρ.ε-homo
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}
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_⁻¹ₖ : Kernel Kernel
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x ⁻¹ₖ = record
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{ element = X.element G.⁻¹

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