JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (04): 76-81.doi: 10.6040/j.issn.1671-9352.0.2014.494

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On Ore extensions of nilpotent p.p.-rings and nilpotent Baer rings

WANG Yao1, ZHANG Jiu-lin1, REN Yan-li2   

  1. 1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China;
    2. School of Mathematics and Information Technology, Nanjing Xiaozhuang University, Nanjing 211171, Jiangsu, China
  • Received:2014-11-07 Revised:2015-03-04 Online:2015-04-20 Published:2015-04-17

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Abstract: The nilpotent p.p., nilpotent Baer and weak McCoy property of the Ore extensions of a ring are investigated. Let R be a quasi-IFP and (α,δ)-condition ring. It is mainly shown that (1) if R is a nilpotent p.p.-ring, then R[x;α,δ] is a nilpotent p.p.-ring; (2) if R is a nilpotent Baer ring, then R[x;α,δ] is a nilpotent Baer ring; (3) R[x;α,δ] is a weak McCoy ring.

Key words: quasi-IFP ring, (α,δ)-condition ring, nilpotent p.p.-ring, weak McCoy ring, nilpotent Baer ring

CLC Number: 

  • O153.3
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[1] LI Min, WANG Yao, REN Yan-li. Power series weak McCoy rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 6-11.
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