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Mathlib/Algebra/Algebra/Basic.lean

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@@ -247,7 +247,9 @@ end FieldDivisionRing
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end algebraMap
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/-- Creating an algebra from a morphism to the center of a semiring. -/
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/-- Creating an algebra from a morphism to the center of a semiring.
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See note [reducible non-instances]. -/
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@[reducible]
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def RingHom.toAlgebra' {R S} [CommSemiring R] [Semiring S] (i : R →+* S)
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(h : ∀ c x, i c * x = x * i c) : Algebra R S where
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smul c x := i c * x
@@ -256,7 +258,9 @@ def RingHom.toAlgebra' {R S} [CommSemiring R] [Semiring S] (i : R →+* S)
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toRingHom := i
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#align ring_hom.to_algebra' RingHom.toAlgebra'
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/-- Creating an algebra from a morphism to a commutative semiring. -/
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/-- Creating an algebra from a morphism to a commutative semiring.
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See note [reducible non-instances]. -/
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@[reducible]
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def RingHom.toAlgebra {R S} [CommSemiring R] [CommSemiring S] (i : R →+* S) : Algebra R S :=
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i.toAlgebra' fun _ => mul_comm _
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#align ring_hom.to_algebra RingHom.toAlgebra

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