CM-field

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