On Geveralized PF Rings
Du Xianneng (Department of Mathematics)
In this paper, we investigate more general rings than PF rings, called fPF rings.We prove the following results:(1) R is a fPF ring if and only if for each a∈R there exists f∈H(R) such that ann_R(f(a)) is a pure ideal of R. (2) Let R be a local ring. Then R is a fPF ring if and only if for every a∈R, there exists f∈H(R) such that f(a) is a non zero divisor or f(a)=0. (3) Ring R is a fPF ring if and only if for every a∈R, there is f∈H(R) such that f(a) is a non zero divisor in each localization Rp or f(a) =0 in each Rp. (4) Ring is a strongly fPF ring, for x∈R, a∈ann_R (x) if and only if f(a)∈ann_R(x), then R is a PF ring. We also provide an example of fPF ring which is not a PF ring.


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