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In algebraic number theory, the narrow class group of a number field ''K'' is a refinement of the class group of ''K'' that takes into account some information about embeddings of ''K'' into the field of real numbers. == Formal definition == Suppose that ''K'' is a finite extension of Q. Recall that the ordinary class group of ''K'' is defined to be : where ''I''''K'' is the group of fractional ideals of ''K'', and ''P''''K'' is the group of principal fractional ideals of ''K'', that is, ideals of the form ''aO''''K'' where ''a'' is a unit of ''K''. The narrow class group is defined to be the quotient : where now ''P''''K''+ is the group of totally positive principal fractional ideals of ''K''; that is, ideals of the form ''aO''''K'' where ''a'' is a unit of ''K'' such that σ(''a'') is ''positive'' for every embedding : 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「narrow class group」の詳細全文を読む スポンサード リンク
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