MathGloss

Let $R$ be a ring with multiplicative identity $1$. A left $R$-module $M$ is an abelian group $(M, +)$ and another operation $\cdot : R\times M \to M$ such that fior all $r,s\in R$ and $x,y\in M$,

1. $r\cdot (x+y) = r\cdot x + r\cdot y$;
2. $(r+s)\dot x = r\cdot x + s\cdot x$;
3. $(rs)\cdot x = r\cdot (s\cdot x)$;
4. $1\cdot x = x$.

The operation $\cdot$ is called scalar multiplication.

Wikidata ID: Q18848

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