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For a commutative ring with unity R , it is proved that R is a P F ‐ring if and only if the annihilator, , for each a ϵ R is a pure ideal in R , Also it is proved that the polynomial ring, R [ X ], is a P F ‐ring if and only if R is a P F ‐ring. Finally, we prove that R is a P P ‐ring if and only if R [ X ] is a PP ‐ring.
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Hasan Al-Ezeh (1986) studied this question.
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