English
If R has CharP p, then FreeAlgebra R X also has CharP p.
Русский
Если у кольца R характеристика p, то у свободного алгебраического кольца FreeAlgebra R X характеристика p.
LaTeX
$$$( \\text{CharP}(R,p) ) \\Rightarrow \\text{CharP}(\\mathrm{FreeAlgebra}(R,X), p)$$$
Lean4
/-- A nontrivial `ℚ`-algebra has characteristic zero.
This cannot be a (local) instance because it would immediately form a loop with the
instance `DivisionRing.toRatAlgebra`. It's probably easier to go the other way: prove `CharZero R`
and automatically receive an `Algebra ℚ R` instance.
-/
theorem charZero [Ring R] [Algebra ℚ R] : CharZero R :=
@CharP.charP_to_charZero R _ (algebraRat.charP_zero R)
