| Armendariz环和斜Armendariz环 |
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| 引用本文： | 郭颖,杜现昆,谢敬然.Armendariz环和斜Armendariz环[J].吉林大学学报(理学版),2005,43(3):253-257. |
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| 作者姓名： | 郭颖 杜现昆 谢敬然 |
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| 作者单位： | (吉林大学 数学学院, 长春 130012) |
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| 基金项目： | 国家自然科学基金(批准号:10471055) |
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| 摘 要： | 讨论Armendariz环的商环是否仍为Armendariz环. 应用
Gauss引理及形式矩阵, 证明了惟一分解整环(UFD)关于主理想的商环是Armendariz环， 给
出了R［x］/(x2-1)为Armendariz环的条件. 将一些Armendariz环的结果推广到斜Armendariz环. 不但推广了已有文献的结论, 而且提供了Armendariz环的新例子.
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| 关 键 词： | Armendariz环 reduced环 斜Armendariz环 惟一分解整环 |
| 文章编号： | 1671-5489(2005)03-0253-05 |
| 收稿时间： | 2004-08-19 |
| 修稿时间： | 2004年8月19日 |
Armendariz Rings and Skew Armendariz Rings |
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| GUO Ying,DU Xian-kun,XIE Jing-ran.Armendariz Rings and Skew Armendariz Rings[J].Journal of Jilin University: Sci Ed,2005,43(3):253-257. |
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| Authors: | GUO Ying DU Xian-kun XIE Jing-ran |
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| Institution: | (College of Mathematics, Jilin University, Changchun 130012, China) |
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| Abstract: | The present paper deals with whether quotient rings of Armendariz rings are also Armendariz rings. By means of Gauss Lemma and formal matrix, it is proved that quotient rings of a unique factorization domain (UFD) with respect to its principal ideals are Armendariz rings, and we present a condition for Rx]/(x 2-1) to be an Armendariz ring. Some results on Armendariz rings are extended to skew Armendariz rings. The paper not only generalizes some results in literature but also provides new examples of Armendariz rings. |
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| Keywords: | Armendariz ring reduced ring skew Armendariz ring unique factorization domain |
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