In mathematics, a CM-field is a particular type of number field, so named for a close connection to the theory of complex multiplication.
In other words, there is a subfield F of K such that K is generated over F by a single square root of an element, say β =
, in such a way that the minimal polynomial of β over the rational number field
For this α should be chosen totally negative, so that for each embedding σ of
into the real number field, σ(α) < 0.
induces an automorphism on the field which is independent of its embedding into