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In mathematics, Arf semigroups are certain subsets of the non-negative integers closed under addition, that were studied by . They appeared as the semigroups of values of Arf rings. A subset of the integers forms a monoid if it includes zero, and if every two elements in the subset have a sum that also belongs to the subset. In this case, it is called a "numerical semigroup". A numerical semigroup is called an Arf semigroup if, for every three elements ''x'', ''y'', and ''z'' with ''z'' = min(''x'', ''y'', and ''z''), the semigroup also contains the element . For instance, the set containing zero and all even numbers greater than 10 is an Arf semigroup. ==References== * *. 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「Arf semigroup」の詳細全文を読む スポンサード リンク
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