mapGL — Mathlib

English

For [FaithfulSMul R S], the function mapGL S is injective.

Русский

При условии FaithfulSMul R S функция mapGL S инъективна.

LaTeX

$$\\mathrm{mapGL} \\text{ is injective given FaithfulSMul } R S$$

Lean4

/-- `mapGL` is the map from the special linear group over `R` to the general linear group over
`S`, where `S` is an `R`-algebra. -/
def mapGL : Matrix.SpecialLinearGroup n R →* Matrix.GeneralLinearGroup n S :=
  toGL.comp (map (algebraMap R S))

Похожие утверждения