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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 Schreier domain ： ウィキペディア英語版 Schreier domain In abstract algebra, a Schreier domain, named after Otto Schreier, is an integrally closed domain where every nonzero element is primal; i.e., whenever ''x'' divides ''yz'', ''x'' can be written as ''x'' = ''x''1 ''x''2 so that ''x''1 divides ''y'' and ''x''2 divides ''z''. An integral domain is said to be pre-Schreier if every nonzero element is primal. A GCD domain is an example of a Schreier domain. The term "Schreier domain" was introduced by P. M. Cohn in 1960s. The term "pre-Schreier domain" is due to Muhammad Zafrullah. In general, an irreducible element is primal if and only if it is a prime element. Consequently, in a Schreier domain, every irreducible is prime. In particular, an atomic Schreier domain is a unique factorization domain; this generalizes the fact that an atomic GCD domain is a UFD. == References == * Cohn, P.M., (Bezout rings and their subrings ), 1967. * Zafrullah, Muhammad, (On a property of pre-Schreier domains ), 1987. 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「Schreier domain」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.