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In algebra, the terms left and right denote the order of a binary operation (usually, but not always called "multiplication") in non-commutative algebraic structures. A binary operation ∗ is usually written in the infix form: : The argument is placed on the left side, and the argument is on the right side. Even if the symbol of the operation is omitted, the order of and does matter unless ∗ is commutative. A two-sided property is fulfilled on both sides. A one-sided property is related to one (unspecified) of two sides. Although terms are similar, left–right distinction in algebraic parlance is not related either to left and right limits in calculus, or to left and right in geometry. == Binary operation as an operator == A binary operation may be considered as a family of unary operators through currying :, depending on as a parameter. It is the family of ''right'' operations. Similarly, : defines the family of ''left'' operations parametrized with . If for some , the left operation is identical, then is called a left identity. Similarly, if , then is a right identity. In ring theory, a subring which is invariant under ''any'' left multiplication in a ring, is called a left ideal. Similarly, a right multiplications-invariant subring is a right ideal. 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「Left and right (algebra)」の詳細全文を読む スポンサード リンク
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