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## 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.
【Fund】： 安徽省教委科研资金资助
【CateGory Index】： O62
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 【Co-references】
 Chinese Journal Full-text Database 5 Hits
 1 Chen Lanqing (Department of Mathematics,Fujian Teachers University,Fuzhou 350007);The Ring of Polynomials over a Normal GPP Ring[J];JOURNAL OF FUJIAN TEACHERS UNIVERSITY(NATURAL SCIENCE);1998-03 2 LI Shan-shan,WANG Ming-yi (College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,China);ON P-FLAT MODULES[J];Journal of Guangxi Normal University(Natural Science);2004-04 3 Chen Lanqing (Dept. of Math. Fujian Normal University,Fuzhou 350007);On Normal Almost PP Rings[J];JOURNAL OF MATHEMATICAL STUDY;1998-02 4 Chen Lanqing(Dept.of Math.,Fujian Normal University,Fuzhou 350007);On Normal GPP Rings[J];JOURNAL OF MATHEMATICAL STUDY;1996-03 5 ZHU Hong-ying (Department of Mathematics,Zhejiang Normal University,Jinhua 321004,China);A Generalized Flat Module[J];Mathematica Applicata;2004-S1
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