finiteType_of_fg — Mathlib

English

If a monoid M is finitely generated, then MonoidAlgebra R M is a finite type R-algebra.

Русский

Если моноид MFinally порожден, то MonoidAlgebra R M конечного типа над R.

LaTeX

$$$\\mathrm{FG}(M) \\Rightarrow \\mathrm{FiniteType}(R,\\,\\mathrm{MonoidAlgebra}(R,M))$$$

Lean4

/-- If a monoid `M` is finitely generated then `MonoidAlgebra R M` is of finite type. -/
instance finiteType_of_fg [CommRing R] [Monoid.FG M] : FiniteType R (MonoidAlgebra R M) :=
  (AddMonoidAlgebra.finiteType_of_fg R (Additive M)).equiv (toAdditiveAlgEquiv R M).symm

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