Remark 5

Suppose that one has $p = p'$ and that the injection $u : M' \to M$ which occurs in the exact sequence of prop. 1 belongs to $J \operatorname{Hom}_A(M', M)$. One then has $p'' = p - 1$. In fact, the assumption implies that the mapping $\operatorname{Ext}_A^i(1_{A/J}, u)$ is zero for every integer $i$; this excludes case a) considered above.