toAlgHom — Mathlib

English

A hom between extensions f: P.Hom P' induces an R-algebra homomorphism f.toAlgHom from P.Ring to P'.Ring.

Русский

Гомоморфизм между расширениями f: P.Hom P' индуцирует R-алгебра-гомоморфизм f.toAlgHom: P.Ring → P'.Ring.

LaTeX

$$$f:\\mathrm{Hom}(P,P')\\Rightarrow f^{\\mathrm{toAlgHom}}:\\ P.Ring \\to_{R} P'.Ring$$$

Lean4

/-- A hom between extensions as an algebra homomorphism. -/
noncomputable def toAlgHom [Algebra R S'] [IsScalarTower R R' S'] (f : Hom P P') : P.Ring →ₐ[R] P'.Ring
    where
  __ := f.toRingHom
  commutes' := by simp [← IsScalarTower.algebraMap_apply]

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