English
If the target Y carries a ring structure and the actions are compatible, the space X→ₑ[σ] Y becomes a ring under pointwise addition and multiplication.
Русский
Если на Y задана кольцевая структура и действия совместимы, то пространство X→ₑ[σ] Y образует кольцо под поком по сумме и произведению.
LaTeX
$$$X \to_{\sigma} Y \text{ is a ring under pointwise operations}$$$
Lean4
instance [SMul M X] [Monoid N] [Semiring Y] [MulSemiringAction N Y] : Semiring (X →ₑ[σ] Y)
where
__ := inferInstanceAs (Monoid _)
__ := inferInstanceAs (AddCommMonoid _)
zero_mul _ := ext fun x ↦ zero_mul _
mul_zero _ := ext fun x ↦ mul_zero _
left_distrib _ _ _ := ext fun x ↦ left_distrib _ _ _
right_distrib _ _ _ := ext fun x ↦ right_distrib _ _ _
