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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Numerical semigroup ： ウィキペディア英語版 Numerical semigroup In mathematics, a numerical semigroup is a special kind of a semigroup. Its underlying set is the set of all nonnegative integers except a finite number and the binary operation is the operation of addition of integers. Also, the integer 0 must be an element of the semigroup. For example, while the set is a numerical semigroup, the set is not because 1 is in the set and 1 + 1 = 2 is not in the set. Numerical semigroups are commutative monoids and are also known as numerical monoids. The definition of numerical semigroup is intimately related to the problem of determining nonnegative integers that can be expressed in the form ''x''1''n''1 + ''x''2 ''n''2 + ... + ''x''''r'' ''n''''r'' for a given set of positive integers and for arbitrary nonnegative integers ''x''1, ''x''2, ..., ''x''''r''. This problem had been considered by several mathematicians like Frobenius (1849 – 1917) and Sylvester (1814 – 1897) at the end of the 19th century. During the second half of the twentieth century, interest in the study of numerical semigroups resurfaced because of their applications in algebraic geometry. == Definition and examples== 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「Numerical semigroup」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.