[[Algebraic element]]
# Roots of a minimal polynomial

Let $A$ be a [[K-monoid]] over $\mathbb{K}$ and $a \in A$ be an [[algebraic element]] with [[Algebraic element|minimal polynomial]] $m_{a}(x) \in \mathbb{K}[x]$.
Then $r \in \mathbb{K}$ is a root of $m_{a}(x)$ iff $a-r 1$ is not invertible in $A$.[^2008] #m/thm/falg 

> [!missing]- Proof
> #missing/proof

  [^2008]: 2008\. [[Sources/@romanAdvancedLinearAlgebra2008|Advanced Linear Algebra]], §18, p. 461

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