ring

《代数学引论》 · 第 42 页

那么 $L$ 就称为一个环。

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《Abstract Algebra》 · 第 223 页 · Section 7.1「Basic Definitions and Examples」，Definition

A ring $R$ is a set together with two binary operations $+$ and $\times$ (called addition and multiplication) satisfying the following axioms: (i) $(R,+)$ is an abelian group, (ii) $\times$ is associative: $(a\times b)\times c=a\times(b\times c)$ for all $a,b,c\in R$, (iii) the distributive laws hold in $R$: for all $a,b,c\in R$, $(a+b)\times c=(a\times c)+(b\times c)$ and $a\times(b+c)=(a\times b)+(a\times c)$.