| Baer环和拟-Baer环的多项式扩张的一点注记 |
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| 引用本文： | 汪小琳,李树海,宋雪梅.Baer环和拟-Baer环的多项式扩张的一点注记[J].纯粹数学与应用数学,2011,27(2):253-255. |
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| 作者姓名： | 汪小琳 李树海 宋雪梅 |
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| 作者单位： | 西北师范大学数学与信息科学学院;兰州城市学院数学学院; |
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| 基金项目： | 甘肃省自然科学基金(3ZS061-A25-015) |
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| 摘 要： | I1和I2分别是环R的一个左理想和右理想,T1=Rx]和T2=Rx,x-1]分别表示多项式环和洛朗多项式环.首先给出两个例子,分别说明了T1I1不一定是T1的左理想与T2L2不一定是T2的右理想.其次给出了环的多项式扩张及洛朗扩张的理想的性质.最后证明了,若RX](Rx,x-1])是拟-Baer环,则R也是拟-...
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| 关 键 词： | 拟-Baer环 多项式环 洛朗多项式环 扩张 |
A note on polynomial extensions of quasi-Baer rings |
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| WANG Xiao-lin,LI Shu-hai,SONG Xue-mei.A note on polynomial extensions of quasi-Baer rings[J].Pure and Applied Mathematics,2011,27(2):253-255. |
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| Authors: | WANG Xiao-lin LI Shu-hai SONG Xue-mei |
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| Institution: | WANG Xiao-lin 1,LI Shu-hai 2,SONG Xue-mei 2(1.College of Mathematics and Information Science,Northwest Normal University,Lanzhou 730070,China,2.School of Mathematics,Lanzhou City University,China) |
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| Abstract: | I1 and I2 be a left ideal and a right ideal of the ring R respectively,T1=Rx] and T2=Rx,x-1]be a polynomial ring and a Laurent polynomial ring respectively.Firstly,the thesis provides two examplesexplaining that T1I1 is not necessarily a left ideal of T1 and T2I2 is not necessarily a right ideal of T2.Secondly,it proves the properties of ideals on polynomial extensions and Laurent extensions of rings by which we showthat R is a quasi-Baer ring if Rx](Rx,x-1]) is a quasi-Baer ring. |
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| Keywords: | quasi-Baer ring polynomial ring Laurent polynomial ring extension |
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