Let R is a PP-ring. we know that any submodule of a torsion-free left R-module is torsion-free; a direct sum of a torsion-free left R-modules is torsion-free.
I do not know the reason of following conclusion: "Since $l(\lambda )$ is finitely generated when principle left ideal $R \lambda$ is projective, we have every right R-module possesses the largest torsion-free factor module".
Here, $l(\lambda)= \left\lbrace r \in R; \lambda r = 0\right\rbrace$
Please help me explain it clearly! Thank you very much!