algebra — Mathlib

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

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