# Tag Archives: dual

## Projectivity and the double dual: Part 2

Let $R$ be an associative ring. If $M$ is a left $R$-module, then the dual module $M^*$ is the right $R$-module ${\rm Hom}(M,R)$. The action of $R$ on this module is given by $(fr)(m) = f(m)r$. We give it a right $R$-module structure since $f$ is a homomorphism of left $R$-modules. Trying to give it […]