right ideal

《近世代数》 · 第 111 页

类似地，可定义环 $R$ 的右理想。

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《Abstract Algebra》 · 第 242 页 · Section 7.3「Ring Homomorphisms and Quotient Rings」，Definition

Let $R$ be a ring, let $I$ be a subset of $R$ and let $r\in R$. (1) $rI=\{ra\mid a\in I\}$ and $Ir=\{ar\mid a\in I\}$. (2) A subset $I$ of $R$ is a left ideal of $R$ if (i) $I$ is a subring of $R$, and (ii) $I$ is closed under left multiplication by elements from $R$, i.e., $rI\subseteq I$ for all $r\in R$. Similarly $I$ is a right ideal if (i) holds and in place of (ii) one has (ii)' $I$ is closed under right multiplication by elements from $R$, i.e., $Ir\subseteq I$ for all $r\in R$.