| 右对称环 |
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| 引用本文： | 李晓伟,任艳丽. 右对称环[J]. 数学理论与应用, 2012, 0(2): 33-38 |
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| 作者姓名： | 李晓伟 任艳丽 |
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| 作者单位： | 南京信息工程大学数学与统计学院;南京晓庄学院数学与信息技术学院 |
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| 基金项目： | 国家自然科学基金项目(11101217);江苏省教育厅自然科学基金项目(11KJB110007) |
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| 摘 要： | 本文在左对称环的基础上提出了右对称环的概念，分别给出了是右对称环但不是左对称环和是左对称环但不是右对称环的例子．证明了（1）如果R是Armendariz环，则R是右对称环的充要条件R[x]是右对称环；（2）如果R是约化环，则R[x]/（x^n）是右对称环，其中（xn）是由xn生成的理想．
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| 关 键 词： | 对称环 右对称环 约化环 Armendariz环 |
Right Symmetric Rings |
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| Li Xiao-wei Ren Yanli. Right Symmetric Rings[J]. Mathematical Theory and Applications, 2012, 0(2): 33-38 |
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| Authors: | Li Xiao-wei Ren Yanli |
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| Affiliation: | Li Xiao-wei Ren Yanli(College of mathematics and statistics of Nanjing University of information science & technology,Nanjing 210044; College of mathematics and information technology of Nanjing xiaozhuang university,Nanjing 211171) |
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| Abstract: | In this paper,we firstly give a definition of right symmetric ring which is just an imitation of the definition of left symmetric ring,and then present some examples that show a right symmetric ring is not necessarily a left symmetric ring,and vice versa.In addition,we prove that(1) if R is an Armendariz ring,then R is a right symmetric ring if and only if R[x] is a right symmetric ring;(2) if R is a reduced ring,then R[x]/(xn) is a right symmetric ring,where(xn)is the ideal generated by xn. |
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| Keywords: | Symmetric ring Right symmetric ring Reduced ring Armendarz ring |
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