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PP- ring

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PP- ring

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"
$l(\lambda)= \{ r \in R; \lambda r = 0\}$

Please help me explain it clearly! Thank you very much!


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