Let be a -module. Then acts on as follows, \begin{align*}n\cdot m &= \underbrace{(1+\cdots + 1)}_{\text{$n$ times}}\cdot m,\\ &= \underbrace{1\cdot m +\cdots +1\cdot m}_{\text{$n$ times}},\\ &=\underbrace{m + \cdots + m}_{\text{$n$ times}}.\end{align*}As it turns out, this is the only possible action of on . A key takeaway about -modules is that there is a bijection between -modules and abelian groups.