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.
出处
《吉林大学学报（理学版）》
CAS
CSCD
北大核心
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)
