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In mathematics, and more specifically in abstract algebra, a rng (or pseudo-ring or non-unital ring) is an algebraic structure satisfying the same properties as a ring, without assuming the existence of a multiplicative identity. The term "rng" (pronounced ''rung'') is meant to suggest that it is a "ring" without "i", i.e. without the requirement for an "identity element". There is no consensus in the community as to whether the existence of a multiplicative identity must be one of the ring axioms (see the history section of the article on rings). The term "rng" was coined to alleviate this ambiguity when people want to refer explicitly to a ring without the axiom of multiplicative identity. A number of algebras of functions considered in analysis are not unital, for instance the algebra of functions decreasing to zero at infinity, especially those with compact support on some (non-compact) space. == Definition == Formally, a rng is a set ''R'' with two binary operations called ''addition'' and ''multiplication'' such that * (''R'', +) is an abelian group, * (''R'', ·) is a semigroup, * Multiplication distributes over addition. Rng homomorphisms are defined in the same way as ring homomorphisms except that the requirement is dropped. That is, a rng homomorphism is a function from one rng to another such that * ''f''(''x'' + ''y'') = ''f''(''x'') + ''f''(''y'') * ''f''(''x'' · ''y'') = ''f''(''x'') · ''f''(''y'') for all ''x'' and ''y'' in ''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「Rng (algebra)」の詳細全文を読む スポンサード リンク
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