English
Let R be a commutative semiring and A a nonunital R-algebra with a star structure. The right embedding a ↦ inr(a) defines a nonunital star-algebra homomorphism from A into the unitization Unitization(R, A).
Русский
Пусть R — коммутативная полугруппа, A — негомоморфная R-алгебра с звездной структурой. Правое вложение a ↦ inr(a) задаёт неединообразный звездный алгебро-гомоморфизм из A в единичизацию Unitization(R, A).
LaTeX
$$$\text{Inr nonunital star-algebra homomorphism } A \to R\text{-unitization }(R,A) \text{ sending } a \mapsto inr(a) \text{ exists and preserves star.}$$$
Lean4
/-- The coercion from a non-unital `R`-algebra `A` to its unitization `Unitization R A`
realized as a non-unital star algebra homomorphism. -/
@[simps!]
def inrNonUnitalStarAlgHom (R A : Type*) [CommSemiring R] [StarAddMonoid R] [NonUnitalSemiring A] [Star A]
[Module R A] : A →⋆ₙₐ[R] Unitization R A
where
toNonUnitalAlgHom := inrNonUnitalAlgHom R A
map_star' := inr_star
