Projective modules over enveloping algebra How could I prove the following statement?
Let $k$ a commutative ring and let $A$ an associative $k$-algebra that is also a projective $k$-module. Then every projective $A\otimes A^{op}$ left module is also a projective $A$-left module (and a projective $A$- right module).

A direct summand of a projective module is projective, and an arbitrary direct sum of projective modules is projective, so it is enough to do this for $P=A\otimes_kA$, and then it is obvious!
