All elements of a finite-dimensional unital associative algebra are algebraic

Let $𝐴$ be a $𝕂$ -monoid. If $𝐴$ is finite dimensional then every element in $𝐴$ is algebraic. #m/thm/falg

Proof

Since the series ${𝑎 𝑖} \infty 𝑖 = 1$ is linearly dependent, the conclusion follows.

#state/tidy | #lang/en | #SemBr