Let \(R\) be a ring and \(M,N\) be $R$-modules. A map \(f\colon M\to N\) is a morphism of modules, or \(R\)-linear map, if \[ f(rm + m') = rf(m) + f(m')\qquad\text{for all } r\in R \text{ and } m,m'\in M. \]
Module morphisms
D-JUYFQ
D-JUYFQ
Let \(R\) be a ring and \(M,N\) be $R$-modules. A map \(f\colon M\to N\) is a morphism of modules, or \(R\)-linear map, if \[ f(rm + m') = rf(m) + f(m')\qquad\text{for all } r\in R \text{ and } m,m'\in M. \]