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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 #-}
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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 #-}
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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 #-}
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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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+
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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
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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 #-}
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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 #-}
@@ -84,5 +84,3 @@ N ∩ M = record
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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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-
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-
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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 #-}
@@ -52,7 +52,7 @@ x ∙ₖ y = record
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{ element = G.ε
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; inKernel = ρ.ε-homo
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}
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-
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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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