[[Algebraic element]]
# All elements of a finite-dimensional unital associative algebra are algebraic

Let $A$ be a [[K-monoid|$\mathbb K$-ring]].
If $A$ is finite dimensional then every element in $A$ is algebraic, since the series $\{a^i\}_{i=1}^\infty$ is linearly dependent. #m/thm/falg


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