English
A component of the additive-algebra equivalence preserves multiplication, i.e., it respects the algebra structure.
Русский
Часть/addах компонент алгебраического эквивалента сохраняет множительную структуру: отображение сохраняет произведение.
LaTeX
$$$\\text{toAdditiveAlgEquiv}(x \\cdot y) = \\text{toAdditiveAlgEquiv}(x) \\cdot \\text{toAdditiveAlgEquiv}(y).$$$
Lean4
/-- The monoid algebra over a semiring `R` generated by the monoid `M`.
It is the type of finite formal `R`-linear combinations of terms of `M`,
endowed with the convolution product. -/
@[to_additive (relevant_arg := 2) /--
The additive monoid algebra over a semiring `R` generated by the additive monoid `M`.
It is the type of finite formal `R`-linear combinations of terms of `M`,
endowed with the convolution product. -/
,
to_additive_dont_translate]
def MonoidAlgebra (R M : Type*) [Semiring R] : Type _ :=
M →₀ R
