  This paper investigates the generalized rank weights, with a definition
implied by the study of the generalized rank weight enumerator. We study rank
metric codes over $L$, where $L$ is a finite Galois extension of a field $K$.
This is a generalization of the case where $K = \mathbb{F}_q$ and $L =
\mathbb{F}_{q^m}$ of Gabidulin codes to arbitrary characteristic. We show
equivalence to previous definitions, in particular the ones by
Kurihara-Matsumoto-Uyematsu, Oggier-Sboui and Ducoat. As an application of the
notion of generalized rank weights, we discuss codes that are degenerate with
respect to the rank metric.
