| T-幂零环的若干扩张 |
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| 引用本文： | 马广琳,王尧,任艳丽. T-幂零环的若干扩张[J]. 山东大学学报(理学版), 2019, 54(12): 68-73. DOI: 10.6040/j.issn.1671-9352.0.2019.135 |
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| 作者姓名： | 马广琳 王尧 任艳丽 |
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| 作者单位： | 1.南京信息工程大学数学与统计学院, 江苏 南京 210044;2.南京晓庄学院信息工程学院, 江苏 南京 211171 |
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| 基金项目： | 江苏省自然科学基金资助项目(BK20181406) |
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| 摘 要： | 研究T-幂零环的一些扩张性质,主要证明了:(1)设R是一个环,α是R上的自同构,则R是左T-幂零环当且仅当R上的斜多项式环R［x;α］是左T-幂零环,当且仅当斜洛朗多项式环R［x,x-1;α］是左T-幂零环;(2)环R是左T-幂零环当且仅当R上的Nagata扩张是左T-幂零环,当且仅当R上的斜三角矩阵环是左T-幂零环。
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| 关 键 词： | T-幂零环 斜多项式环 斜洛朗多项式环 Nagata 扩张 斜三角矩阵环 |
Some extensions of T-nilpotent rings |
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| MA Guang-lin,WANG Yao,REN Yan-li. Some extensions of T-nilpotent rings[J]. Journal of Shandong University, 2019, 54(12): 68-73. DOI: 10.6040/j.issn.1671-9352.0.2019.135 |
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| Authors: | MA Guang-lin WANG Yao REN Yan-li |
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| Affiliation: | 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 |
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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. |
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| Keywords: | T-nilpotent ring skew polynomial ring skew Laurent polynomial ring Nagata extension skew triangular matrix ring |
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