Past exam of the algebra course of the University of Oxford / 2011 / 3 / c / ii / Solution

On the same basis, $Y=D^2$ kills $v,u$ and sends $w$ to $16w$. Explicitly,Thus all three basis lines are submodules after restriction of scalars, andEach summand is a simple module, hence an indecomposable module. Squaring has destroyed the length-two nilpotent Jordan chain.