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In abstract algebra, the field of fractions of an integral domain is the smallest field in which it can be embedded. The elements of the field of fractions of the integral domain are equivalence classes (see the construction below) written as with and in and . The field of fractions of is sometimes denoted by or . Mathematicians refer to this construction as the field of fractions, fraction field, field of quotients, or quotient field. All four are in common usage. The expression "quotient field" may sometimes run the risk of confusion with the quotient of a ring by an ideal, which is a quite different concept. == Examples == * The field of fractions of the ring of integers is the field of rationals, . * Let be the ring of Gaussian integers. Then , the field of Gaussian rationals. * The field of fractions of a field is canonically isomorphic to the field itself. * Given a field , the field of fractions of the polynomial ring in one indeterminate (which is an integral domain), is called the ' or ''field of rational fractions'' and is denoted . 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「Field of fractions」の詳細全文を読む スポンサード リンク
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