The cyclic flats of a q-matroid

In this paper we develop the theory of cyclic flats of q-matroids. We show that the cyclic flats, together with their ranks, uniquely determine a q-matroid and hence derive a new q-cryptomorphism. We introduce the notion of \(\mathbb {F}_{q^m}\) ${\mathbb{F}}_{q^m}$ -independence of an \(\mathbb {F}_q\) ${\mathbb{F}}_q$ -subspace of \(\mathbb {F}_q^n\) ${\mathbb{F}}_q^n$ and we show that q-matroids generalize this concept, in the same way that matroids generalize the notion of linear independence of vectors over a given field.