semisimple projective modules over von Neumann non-regular rings I am searching the example of semisimple projective modules over von Neumann non-regular ring. I already have an example, it is $\mathbb{Z}_{p}$ - $\mathbb{Z}_{p}$ with $p$ prime number, this is a semisimple projective module but over von Neumann regular ring. Can someone help me ? Thank you.

Every semisimple ring is von Neumann regular, and every module over such a ring has the property you seek.
You're welcome.

