It is well known that if $mbox{Ext}^1_{A}(P,A/I)=0$ for all $I,$ then $mbox{Ext}^i_{A}(P,A/I)=0$ for all $i$ and for all $I $and $P$ is projective. We can also characterize a projective module $P$ by his trace ideal denoted $t(P),$ we can then for all projective module $P$ the following relations: i) $Pt(P)=P.$ ii) $t(P)^2=t(P).$
