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8 changes: 6 additions & 2 deletions Mathlib/Algebra/Algebra/Basic.lean
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Expand Up @@ -247,7 +247,9 @@ end FieldDivisionRing

end algebraMap

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

/-- Creating an algebra from a morphism to a commutative semiring. -/
/-- Creating an algebra from a morphism to a commutative semiring.
See note [reducible non-instances]. -/
@[reducible]
def RingHom.toAlgebra {R S} [CommSemiring R] [CommSemiring S] (i : R →+* S) : Algebra R S :=
i.toAlgebra' fun _ => mul_comm _
#align ring_hom.to_algebra RingHom.toAlgebra
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