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In mathematics, a CM-field is a particular type of number field, so named for a close connection to the theory of complex multiplication. Another name used is J-field. The abbreviation "CM" was introduced by . ==Formal definition== A number field ''K'' is a CM-field if it is a quadratic extension ''K''/''F'' where the base field ''F'' is totally real but ''K'' is totally imaginary. I.e., every embedding of ''F'' into lies entirely within , but there is no embedding of ''K'' into . 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 has all its roots non-real complex numbers. For this α should be chosen ''totally negative'', so that for each embedding σ of into the real number field, σ(α) < 0. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「CM-field」の詳細全文を読む スポンサード リンク
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