English
If S is a subsemiring of R and A is an algebra over R, then A inherits a natural structure of an S-algebra by composing the inclusion S → R with the original algebra map R → A.
Русский
Если S — подпол semiring R, а A — R-алгебра, то A inherits естественную структуру S-алгебры, задаваемую через композицию S ↪ R → A.
LaTeX
$$Algebra S A with algebraMap_SA := (algebraMap R A) ∘ S.subtype$$
Lean4
instance _root_.PUnit.algebra : Algebra R PUnit.{v + 1}
where
algebraMap :=
{ toFun _ := PUnit.unit
map_one' := rfl
map_mul' _ _ := rfl
map_zero' := rfl
map_add' _ _ := rfl }
commutes' _ _ := rfl
smul_def' _ _ := rfl