Rank of multivariate rational function field #
theorem
MvRatFunc.rank_eq_max_lift
{σ : Type u}
{F : Type v}
[Field F]
[Nonempty σ]
:
Module.rank F (FractionRing (MvPolynomial σ F)) = max (max (Cardinal.lift.{u, v} (Cardinal.mk F)) (Cardinal.lift.{v, u} (Cardinal.mk σ))) Cardinal.aleph0