Vector space/Flag/Successive quotients/Exercise

Let

${}0=V_{0}\subset V_{1}\subset \ldots \subset V_{n-1}\subset V_{n}=V\,$

be a flag in a finite-dimensional ${}K$-vector space ${}V$. Show that

${}V_{i+1}/V_{i}\cong K\,$

holds for ${}i=0,\ldots ,n-1$.

Create a solution