| 翻訳と辞書 |
| Division algebra ： ウィキペディア英語版 |
Division algebra
In the field of mathematics called abstract algebra, a division algebra is, roughly speaking, an algebra over a field in which division is possible.
==Definitions==
Formally, we start with an algebra ''D'' over a field, and assume that ''D'' does not just consist of its zero element. We call ''D'' a division algebra if for any element ''a'' in ''D'' and any non-zero element ''b'' in ''D'' there exists precisely one element ''x'' in ''D'' with ''a'' = ''bx'' and precisely one element ''y'' in ''D'' such that ''a'' = ''yb''.
For associative algebras, the definition can be simplified as follows: an associative algebra over a field is a division algebra if and only if it has a multiplicative identity element 1≠0 and every non-zero element ''a'' has a multiplicative inverse (i.e. an element ''x'' with ''ax'' = ''xa'' = 1).
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「Division algebra」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.
|
|