Corollary 1

Let P be a projective A-module. Suppose that P is finitely generated or that the radical $\mathfrak{r}$ of A is a nilpotent two-sided ideal. Denote the canonical mapping from P to $P/\mathfrak{r}P$ by $u$. Then $(P, u)$ is a projective cover of $P/\mathfrak{r}P$.