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Statements

Subject Item
dbr:Noncommutative_ring
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非可換環 Okommutativ ring Noncommutative ring حلقة غير تبادلية
rdfs:comment
In mathematics, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exist a and b in the ring such that ab and ba are different. Equivalently, a noncommutative ring is a ring that is not a commutative ring. Noncommutative algebra is the part of ring theory devoted to study of properties of the noncommutative rings, including the properties that apply also to commutative rings. Although some authors do not assume that rings have a multiplicative identity, in this article we make that assumption unless stated otherwise. 数学、特に現代代数学と環論において、非可換環（ひかかんかん、英: noncommutative ring）とは乗法が可換ではない環である。つまり、a•b ≠ b•a なる R の元 a, b が存在する。非可換環論 (noncommutative algebra) は可換とは限らない環に適用できる結果の研究であるが、この分野の多くの重要な結果は特別な場合として可換環にも適用できる。 في الرياضيات، وبالتحديد في الجبر التجريدي، حلقة غير تبادلية (بالإنجليزية: Noncommutative ring)‏ هي حلقة حيث لا تشترط في عملية الجداء (أي العملية الثانية المعرِّفة للحلقة) خاصية التبادلية. Inom matematiken, speciellt inom abstrakta algebran och ringteori, är en okommutativ ring en ring vars multiplikation inte är kommutativ; i andra ord finns det element a och b av R med a·b ≠ b·a. Okommutativ algebra är studien av okommutativa ringar; många resultat i detta område gäller dock även för kommutativa ringar.
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في الرياضيات، وبالتحديد في الجبر التجريدي، حلقة غير تبادلية (بالإنجليزية: Noncommutative ring)‏ هي حلقة حيث لا تشترط في عملية الجداء (أي العملية الثانية المعرِّفة للحلقة) خاصية التبادلية. In mathematics, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exist a and b in the ring such that ab and ba are different. Equivalently, a noncommutative ring is a ring that is not a commutative ring. Noncommutative algebra is the part of ring theory devoted to study of properties of the noncommutative rings, including the properties that apply also to commutative rings. Sometimes the term noncommutative ring is used instead of ring to refer to a unspecified ring which is not necessarily commutative, and hence may be commutative. Generally, this is for emphasizing that the studied properties are not restricted to commutative rings, as, in many contexts, ring is used as a shortcut for commutative ring. Although some authors do not assume that rings have a multiplicative identity, in this article we make that assumption unless stated otherwise. 数学、特に現代代数学と環論において、非可換環（ひかかんかん、英: noncommutative ring）とは乗法が可換ではない環である。つまり、a•b ≠ b•a なる R の元 a, b が存在する。非可換環論 (noncommutative algebra) は可換とは限らない環に適用できる結果の研究であるが、この分野の多くの重要な結果は特別な場合として可換環にも適用できる。 Inom matematiken, speciellt inom abstrakta algebran och ringteori, är en okommutativ ring en ring vars multiplikation inte är kommutativ; i andra ord finns det element a och b av R med a·b ≠ b·a. Okommutativ algebra är studien av okommutativa ringar; många resultat i detta område gäller dock även för kommutativa ringar.
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