JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (12): 68-73.doi: 10.6040/j.issn.1671-9352.0.2019.135

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Some extensions of T-nilpotent rings

MA Guang-lin1, WANG Yao1, REN Yan-li2*   

  1. 1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China;
    2. School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, Jiangsu, China
  • Published:2019-12-11

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Abstract: Some extension properties of T-nilpotent rings are investigated. It is mainly proved that(1)If R is a ring and α an automorphism of R, then R is a left T-nilpotent ring if and only if the skew polynomial ring R［x;α］ over R is a left T-nilpotent ring, if and only if the skew Laurent polynomial ring R［x,x-1;α］ is a left T-nilpotent ring;(2)R is a left T-nilpotent ring if and only if the Nagata extension over R is a left T-nilpotent ring, if and only if the skew triangular matrix ring over R is a left T-nilpotent ring.

Key words: T-nilpotent ring, skew polynomial ring, skew Laurent polynomial ring, Nagata extension, skew triangular matrix ring

CLC Number: 

  • O153.3
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[1] WANG Yao1, JIANG Mei-mei1, REN Yan-li2*. Some properties of skew polynomial rings#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(06): 40-45.
[2] ZHANG Wan-ru. Skew nil McCoy rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 57-62.
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