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