Indecomposable modules for a cyclic p-group
= Indecomposable modules for a cyclic p-group
{title2=$V_i=k[t]/(t^i)$}
For $P$ cyclic of order $q=p^n$ in characteristic $p$, its <group algebra> is $k[t]/(t^q)$. The nilpotent <Jordan normal form> classifies its indecomposable finite-dimensional modules as $V_i$, $1\leq i\leq q$. A module homomorphism $V_i\to V_j$ is determined by an element annihilated by $t^i$, so its dimension is $\min(i,j)$.