module

《代数学引论》 · 第 161 页

则 $M$ 叫做环 $R$ 上的一个左模或叫做一个左 $R$-模。

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《Abstract Algebra》 · 第 337 页 · Section 10.1「Basic Definitions and Examples」，Definition

Let $R$ be a ring (not necessarily commutative nor with $1$). A left $R$-module or a left module over $R$ is a set $M$ together with (1) a binary operation $+$ on $M$ under which $M$ is an abelian group, and (2) an action of $R$ on $M$ denoted by $rm$ which satisfies $(r+s)m=rm+sm$, $(rs)m=r(sm)$ and $r(m+n)=rm+rn$. If the ring $R$ has a $1$ we impose the additional axiom $1m=m$.