What conditions to you need to put on your ring to guarantee that the indecomposable projective modules are all finitely generated?
Edit: I was hoping there was some general result for this. If your ring is Krull-Remack-Schmidt then the indecomposable projective modules are generated by an idempotent in your ring so they are finitely generated.
I don't know of any rings in which they are not finitely generated, but I fear I'm not creative enough (if it's true for all rings that would be great too though).