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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 Glossary of ring theory ： ウィキペディア英語版 Glossary of ring theory Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This is a glossary of some terms of the subject. ==Definition of a ring== ;ring : A ''ring'' is a set ''R'' with two binary operations, usually called addition (+) and multiplication (×), such that ''R'' is an abelian group under addition, ''R'' is a monoid under multiplication, and multiplication is both left and right distributive over addition. Rings are assumed to have multiplicative identities unless otherwise noted. The additive identity is denoted by 0 and the multiplicative identity by 1. (''Warning'': some books, especially older books, use the term "ring" to mean what here will be called a rng; i.e., they do not require a ring to have a multiplicative identity.) ; subring : A subset ''S'' of the ring (''R'',+,×) which remains a ring when + and × are restricted to ''S'' and contains the multiplicative identity 1 of ''R'' is called a ''subring'' of ''R''. 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「Glossary of ring theory」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.