English
If M is an AddCommMonoid, then AddMonoid.End(M) carries a semiring structure (pointwise operations).
Русский
Если M — AddCommMonoid, то AddMonoid.End(M) имеет структуру полуг ring (пунктуальная по элементам).
LaTeX
$$End(M) is a Semiring when M is AddCommMonoid.$$
Lean4
instance instSemiring [AddCommMonoid M] : Semiring (AddMonoid.End M) :=
{ AddMonoid.End.instMonoid M, AddMonoidHom.instAddCommMonoid, AddMonoid.End.instAddMonoidWithOne M with
zero_mul := fun _ => AddMonoidHom.ext fun _ => rfl,
mul_zero := fun _ => AddMonoidHom.ext fun _ => AddMonoidHom.map_zero _,
left_distrib := fun _ _ _ => AddMonoidHom.ext fun _ => AddMonoidHom.map_add _ _ _,
right_distrib := fun _ _ _ => AddMonoidHom.ext fun _ => rfl }
