: $(0)$ $M_R$ is a p.p.-module if and only if $M[x;\sigma]_{R[x;\sigma]}$ is a p.p.-module, $(0)$ Let $\sigma\in Aut(R)$, then $M_R$ is a p.p.-module if and only if $M[x,x^{-0};\sigma]_{R[x,x^{-0};\sigma]}$ is a p.p.-module.  