Armendariz环和斜Armendariz环  

Armendariz Rings and Skew Armendariz Rings

作　　者：郭颖[1] 杜现昆[1] 谢敬然[1] 

机构地区：[1]吉林大学数学学院数学系,长春130012

出　　处：《吉林大学学报（理学版）》2005年第3期253-257,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10471055)

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.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 R[x]/(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.

关 键 词：ARMENDARIZ环 REDUCED环 斜ARMENDARIZ环 惟一分解整环 

分 类 号：O153.3[理学—数学]