MathGloss

Let $M$ and $N$ be modules over the ring $R$. A module homomorphism between $M$ and $N$ is a function $f:M\to N$ such that for any $x,y \in M$ and $r\in R$,

1. $f(x+y) = f(x) + f(y)$
2. $f(rx) = rf(x)$ where the operation in (2) is the scalar multiplication.

If a module homomorphism is bijective, then it is an isomorphism of modules.

Wikidata ID: Q215111

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