# Multiplication on the left/right as additive automorphisms #

In this file we define AddAut.mulLeft and AddAut.mulRight.

See also AddMonoidHom.mulLeft, AddMonoidHom.mulRight, AddMonoid.End.mulLeft, and AddMonoid.End.mulRight for multiplication by R as an endomorphism instead of multiplication by Rˣ as an automorphism.

@[simp]
theorem AddAut.mulLeft_apply_symm_apply {R : Type u_1} [inst : ] (x : Rˣ) :
@[simp]
theorem AddAut.mulLeft_apply_apply {R : Type u_1} [inst : ] (x : Rˣ) :
∀ (a : R), ↑(AddAut.mulLeft x) a = x a
def AddAut.mulLeft {R : Type u_1} [inst : ] :

Left multiplication by a unit of a semiring as an additive automorphism.

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