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In mathematics, a tower of fields is a sequence of field extensions : The name comes from such sequences often being written in the form : A tower of fields may be finite or infinite. ==Examples== * is a finite tower with rational, real and complex numbers. *The sequence obtained by letting ''F''0 be the rational numbers Q, and letting :: :(i.e. ''F''''n''+1 is obtained from ''F''''n'' by adjoining a 2''n'' th root of 2) is an infinite tower. *If ''p'' is a prime number the ''p'' th cyclotomic tower of Q is obtained by letting ''F''0 = Q and ''F''''n'' be the field obtained by adjoining to Q the ''pn'' th roots of unity. This tower is of fundamental importance in Iwasawa theory. *The Golod–Shafarevich theorem shows that there are infinite towers obtained by iterating the Hilbert class field construction to a number field. 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「Tower of fields」の詳細全文を読む スポンサード リンク
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