| 对称环的扩张 |
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| 引用本文： | 王占平.对称环的扩张[J].数学研究及应用,2007,27(2):229-235. |
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| 作者姓名： | 王占平 |
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| 作者单位： | 西北师范大学数学系,甘肃,兰州,730070 |
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| 摘 要： | 本文首先考虑了对称环的性质和基本的扩张．其次讨论了几种多项式环的对称性,且证明了:如果R是约化环,则Rx]／(xn)是对称环,其中(xn)是由xn生成的理想,n是一个正整数．最后证明了:对一个右Ore环R,R是对称环当且仅当R的古典右商环Q是对称环．
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| 关 键 词： | 对称环 平凡扩张 多项式环 古典右商环 |
| 文章编号： | 1000-341X(2007)02-0229-07 |
| 收稿时间： | 2005/3/24 0:00:00 |
| 修稿时间： | 3/7/2006 12:00:00 AM |
Extensions of Symmetric Rings |
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| WANG Zhan-ping.Extensions of Symmetric Rings[J].Journal of Mathematical Research with Applications,2007,27(2):229-235. |
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| Authors: | WANG Zhan-ping |
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| Institution: | Department of Mathematics, Northwest Normal University, Lanzhou 730070, China |
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| Abstract: | We first consider properties and basic extensions of symmetric rings. We next axgue about the symmetry of some kinds of polynomial rings, and show that if R is a reduced ring then Rx]/(xn) is a symmetric ring, where (xn) is the ideal generated by xn and n is a positive integer. Consequently, we prove that for a right Ore ring R with Q its classical right quotient ring, R is symmetric if and only if Q is symmetric. |
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| Keywords: | symmetric ring trivial extension polynomial ring classical right quotient ring |
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