Armendariz环和斜Armendariz环

• 数学 • 下一篇

Armendariz环和斜Armendariz环

郭颖, 杜现昆, 谢敬然

(吉林大学数学学院, 长春 130012)

收稿日期:2004-08-19 修回日期:2004-12-01 出版日期:2005-05-26 发布日期:2005-05-26
通讯作者: 杜现昆

Armendariz Rings and Skew Armendariz Rings

GUO Ying, DU Xian-kun， XIE Jing-ran

(College of Mathematics, Jilin University, Changchun 130012, China)

Received:2004-08-19 Revised:2004-12-01 Online:2005-05-26 Published:2005-05-26
Contact: DU Xian-kun

摘要/Abstract

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.

关键词: Armendariz环, reduced环, 斜Armendariz环, 惟一分解整环

Abstract: The present paper deals with whether quotient rings of Armendariz rings are also Armendariz rings. By means of Gauss Lemma and formal m atrix, it is proved that quotient rings of a unique factorization domain (UFD) w ith respect to its princ ipal ideals are Armendariz rings, and we present a condition for R［x］/ (x²-1) to be an Armendariz ring. Some results on Armendariz rings are extende d to skew Armendariz rings. The paper not only generalizes some results in literature but also provides new examples of Armendariz rings.

Key words: Armendariz ring, reduced ring, skew Armendariz ring, u nique factorization domain

中图分类号:

O153.3

郭颖, 杜现昆, 谢敬然. Armendariz环和斜Armendariz环[J]. J4, 2005, 43(03): 253-257.

GUO Ying, DU Xian-kun， XIE Jing-ran. Armendariz Rings and Skew Armendariz Rings[J]. J4, 2005, 43(03): 253-257.

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