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lines changed Original file line number Diff line number Diff line change @@ -11,21 +11,20 @@ open import Algebra.Ideal using (Ideal)
1111
1212module Algebra.Construct.Quotient.Ring {c ℓ} (R : Ring c ℓ) {c′ ℓ′} (I : Ideal R c′ ℓ′) where
1313
14+ open import Algebra.Morphism.Structures using (IsRingHomomorphism)
15+ open import Algebra.Properties.Ring R
16+ open import Algebra.Structures
17+ open import Level
18+
1419open Ring R
1520private module I = Ideal I
1621open I using (ι; normalSubgroup)
1722
1823open import Algebra.Construct.Quotient.Group +-group normalSubgroup public
1924 using (_≋_; _by_; ≋-refl; ≋-sym; ≋-trans; ≋-isEquivalence; ≈⇒≋; quotientIsGroup; quotientGroup; π; π-surjective)
2025 renaming (≋-∙-cong to ≋-+-cong; ≋-⁻¹-cong to ≋‿-‿cong)
21-
2226open import Algebra.Definitions _≋_
23- open import Algebra.Morphism.Structures using (IsRingHomomorphism)
2427open import Algebra.Properties.Semiring semiring
25- open import Algebra.Properties.Ring R
26- open import Algebra.Structures
27- open import Function.Definitions using (Surjective)
28- open import Level
2928open import Relation.Binary.Reasoning.Setoid setoid
3029
3130≋-*-cong : Congruent₂ _*_
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