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In mathematics, more specifically in abstract algebra, the concept of integrally closed has two meanings, one for groups and one for rings. ==Commutative rings== (詳細はintegral closure of in . That is, for every monic polynomial ''f'' with coefficients in , every root of ''f'' belonging to ''S'' also belongs to . Typically if one refers to a domain being integrally closed without reference to an overring, it is meant that the ring is integrally closed in its field of fractions. If the ring is not a domain, typically being integrally closed means that every local ring is an integrally closed domain. Sometimes a domain that is integrally closed is called "normal" if it is integrally closed and being thought of as a variety. In this respect, the normalization of a variety (or scheme) is simply the of the integral closure of all of the rings. 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「integrally closed」の詳細全文を読む スポンサード リンク
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