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<div>抽象代数学において、[[環 (数学)|環]] ''R'' の元 ''a'' は、''ax''=0 となる ''x''≠0 が存在するとき、'''左零因子'''（ひだりれいいんし、ひだりぜろいんし、{{lang-en-short|left zero divisor}}）と呼ばれる<ref>0を左零因子から除く人もいる。</ref>。これは、''x'' を ''ax'' に送る ''R'' から ''R'' への写像が単射でないことと同値である<ref>See Bourbaki, p.&nbsp;98.</ref>。同様に、環の元 ''a'' が'''右零因子'''とは、ある ''y'' ≠ 0 が存在して ''ya''=0 となることである。これは環における因子の特別な場合である。左または右零因子である元は単に'''零因子'''と呼ばれる<ref>See Lanski (2005).</ref>。左かつ右零因子である元 ''a'' は'''両側零因子'''（two-sided zero divisor）と呼ばれる（''ax'' = 0 となる零でない ''x'' は ''ya'' = 0 となる零でない ''y'' とは異なるかもしれない）。環が可換であれば左零因子と右零因子は同じである。<br />
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環の零因子でない元は'''正則'''である（regular）または'''非零因子'''（non-zero-divisor）と呼ばれる。0でない零因子は'''0でない零因子'''（nonzero zero divisor）または'''非自明な零因子'''（nontrivial zero divisor）と呼ばれる。<br />
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== 脚注 ==<br />
<references/><br />
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== 参考文献 ==<br />
* {{citation |author= [[N. Bourbaki]] |title=Algebra I, Chapters 1–3 |publisher=Springer-Verlag |year=1989}}.<br />
* {{citation |author= Charles Lanski |year=2005 |title=Concepts in Abstract Algebra |publisher=American Mathematical Soc. |page=342 }}<br />
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==関連項目==<br />
* [[零元]]<br />
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{{DEFAULTSORT:れいいんし}}<br />
[[Category:0]]<br />
[[Category:数学に関する記事]]</div>60.61.248.186 Warning: Cannot modify header information - headers already sent by (output started at /home/users/1/sub.jp-asate/web/wiki/extensions/HeadScript/HeadScript.php:3) in /home/users/1/sub.jp-asate/web/wiki/includes/WebResponse.php on line 46