Let $\ell$ be an odd prime number,$\zeta_{\ell}:=e^{2\pi i/\ell}$, $F:=\mathbb{Q}(\zeta_{\ell})$ be a cyclotomic field, $\mathcal{O}_F$ be its integer ring and $\lambda:=1-\zeta_{\ell}$.
[Ireland-Rosen] "A Classical Introduction to Modern Number Theory" introduce following concept in chapter 14 section 2.
Definition $\alpha\in \mathcal{O}_F$ is called primary if it is not a unit and prime to $\ell$ and there is some integer $n\in\mathbb{Z}$ such that $\alpha\equiv n\pmod{\lambda^2}$
I heard that this concept can be described in terms of $\lambda$ adic number. Can anyone do that? If you can, please explain why.