Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 138 / 1 / d / ii / Solution

For the left regular module, the radical series of a module is obtained by multiplying by powers of the Jacobson radical:Products of matrix units show thatwith $N^0=A$ and $N^n=0$. Thus each step removes one subdiagonal, and the Loewy length of ${}_{A}A$ is $n$.