@@ -68,7 +68,7 @@ universe uS uA uB
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then their quotients are also `R`-equivalent.
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(Special case of the third isomorphism theorem.)-/
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- def algEquiv_quot_algEquiv
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+ def algEquivQuotAlgEquiv
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{R : Type u} [CommSemiring R] {A B : Type v} [Semiring A] [Semiring B]
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[Algebra R A] [Algebra R B] (f : A ≃ₐ[R] B) (rel : A → A → Prop ) :
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RingQuot rel ≃ₐ[R] RingQuot (rel on f.symm) :=
@@ -83,16 +83,20 @@ def algEquiv_quot_algEquiv
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fun x y h ↦ by apply RingQuot.mkAlgHom_rel; simpa⟩))
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(by ext b; simp) (by ext a; simp)
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+ @[deprecated (since := "2024-12-07")] alias algEquiv_quot_algEquiv := algEquivQuotAlgEquiv
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+
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/--If two (semi)rings are equivalent and their quotients by a relation `rel` are defined,
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then their quotients are also equivalent.
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(Special case of `algEquiv_quot_algEquiv` when `R = ℕ`, which in turn is a special
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case of the third isomorphism theorem.)-/
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- def equiv_quot_equiv {A B : Type v} [Semiring A] [Semiring B] (f : A ≃+* B) (rel : A → A → Prop ) :
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+ def equivQuotEquiv {A B : Type v} [Semiring A] [Semiring B] (f : A ≃+* B) (rel : A → A → Prop ) :
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RingQuot rel ≃+* RingQuot (rel on f.symm) :=
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let f_alg : A ≃ₐ[ℕ] B :=
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AlgEquiv.ofRingEquiv (f := f) (fun n ↦ by simp)
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- algEquiv_quot_algEquiv f_alg rel |>.toRingEquiv
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+ algEquivQuotAlgEquiv f_alg rel |>.toRingEquiv
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+
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+ @[deprecated (since := "2024-12-07")] alias equiv_quot_equiv := equivQuotEquiv
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end RingQuot
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@@ -143,11 +147,14 @@ theorem rel_id (i : I) : rel R A (ι R <| lof R I A i 1) 1 := rel.id
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@[reducible] def _root_.LinearAlgebra.FreeProduct := RingQuot <| FreeProduct.rel R A
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/--The free product of the collection of `R`-algebras `A i`, as a quotient of `PowerAlgebra R A`-/
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- @[reducible] def _root_.LinearAlgebra.FreeProduct_ofPowers := RingQuot <| FreeProduct.rel' R A
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+ @[reducible] def _root_.LinearAlgebra.FreeProductOfPowers := RingQuot <| FreeProduct.rel' R A
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+
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+ @[deprecated (since := "2024-12-07")]
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+ alias _root_.LinearAlgebra.FreeProduct_ofPowers := LinearAlgebra.FreeProductOfPowers
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/--The `R`-algebra equivalence relating `FreeProduct` and `FreeProduct_ofPowers`-/
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- noncomputable def equivPowerAlgebra : FreeProduct_ofPowers R A ≃ₐ[R] FreeProduct R A :=
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- RingQuot.algEquiv_quot_algEquiv
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+ noncomputable def equivPowerAlgebra : FreeProductOfPowers R A ≃ₐ[R] FreeProduct R A :=
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+ RingQuot.algEquivQuotAlgEquiv
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(FreeProduct.powerAlgebra_equiv_freeAlgebra R A |>.symm) (FreeProduct.rel R A)
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|>.symm
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