we begin by revisiting the definition and some of the properties of the minimal polynomial of an element of a finite-dimensional power-associative algebra $\cal a$ over an arbitrary field $\mathbb{f}$. our main observation is that $p_a$, the minimal polynomial of $a\in\cal a$, may depend not only on $a$, but also on the underlying algebra. restricting attention to the case where $\mathbb{f}$ is either $\mathbb{r}$ or $\mathbb{c}$, we proceed to define $r(a)$, the {\it radius} of an element $a$ in $\cal a$, to be the largest root in absolute value of the minimal polynomial of $a$. as it is, $r$ possesses some of the familiar properties of the classical spectral radius. in particular, $r$ is a continuous function on $\cal a$. in the third part of the talk we discuss stability of subnorms acting on subsets of finite-dimensional power-associative algebras. following a brief survey, we enhance our understanding of the subject with the help of our findings about the radius $r$. our main new result states that if $\cal s$, a subset of an algebra $\cal a$, satisfies certain assumptions, and $f$ is a continuous subnorm on $\cal s$, then $f$ is stable on $\cal s$ if and only if $f$ majorizes the radius \nolinebreak$r$.