Q:

Meaning of $\min _ {b, \mathbb F }$

Say that $b \in \mathbb K$ which is a field. And $\mathbb F $ is also a field.
What does the notation $\min _ {b, \mathbb F }$ mean?  Specifically, I've encountered this in the following context:

Suppose $\mathbb{K}/\mathbb{F}$ is an arbitrary finite field extension.  Prove that if $f\in\mathbb{F}[x]$ is irreducible of degree at least $1$ and $a\in\mathbb{K}$ is a root of $f$ then $\min_{a,\mathbb{F}}=\frac{1}{c}f$ where $c$ is the leading coefficient of $f$.

A:

I've never seen this notation before, but from context it seems like it is supposed to denote the minimal polynomial of $b$ over $\mathbb{F}$ (assuming $\mathbb{K}$ is an extension of $\mathbb{F}$).

