  In this paper I consider polynomial composites with the coefficients from
$K\subset L$. We already know many properties, but we do not know the answer to
the question of whether there is a relationship between composites and field
extensions. I present the characterization of some known field extensions in
terms of polynomial composites. This paper contains the opening problem of
characterization of ideals in polynomial composites with respect to various
field extensions. I also present the full possible characterization of certain
field extensions.
