Let

*a* be an element of some

field *F* and let

*k* be a

subfield of

*F*. Suppose that

*a* is a root of some nonzero
polynomial in

*k[x]*. The minimal

polynomial of

*a* over

*k*
is the monic (i.e. x

^{n}+lower degree terms)
polynomial of least degree in

*k[x]* that has

*a* as a

root.

Here are some properties of the minimal polynomial