@@ -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
19- using (_≋_; _by_; ≋-refl; ≋-sym; ≋-trans; ≋-isEquivalence; ≈⇒≋; quotientIsGroup; quotientGroup; project; project -surjective)
24+ 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 _*_
@@ -69,8 +68,8 @@ quotientIsRing = record
6968quotientRing : Ring c (c ⊔ ℓ ⊔ c′)
7069quotientRing = record { isRing = quotientIsRing }
7170
72- project -isHomomorphism : IsRingHomomorphism rawRing quotientRawRing project
73- project -isHomomorphism = record
71+ π -isHomomorphism : IsRingHomomorphism rawRing quotientRawRing π
72+ π -isHomomorphism = record
7473 { isSemiringHomomorphism = record
7574 { isNearSemiringHomomorphism = record
7675 { +-isMonoidHomomorphism = record
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