关于拟正则Armendariz环  

On Quasi-regular Armendariz Rings

作　　者：宋雪梅 SONG Xue-mei(Lanzhou City University,Lanzhou 730070,China)

机构地区：[1]兰州城市学院信息工程学院,甘肃兰州730070

出　　处：《金陵科技学院学报》2023年第1期88-92,共5页Journal of Jinling Institute of Technology

基　　金：国家自然科学基金项目(11861055)。

摘　　要：引入拟正则Armendariz环并研究其性质。证明弱Armendariz环是拟正则Armendariz环,直积∏i∈I R i是拟正则Armendariz环当且仅当每个环R i(i∈I)是拟正则Armendariz环,同时证明R是拟正则Armendariz环当且仅当上三角矩阵环T n(R)(n≥2)是拟正则Armendariz环,并通过例子说明任意环R上的全矩阵环M n(R)(n≥2)不是拟正则Armendariz环。Quasi-regular Armendariz rings are introduced and their properties are studied.It is proved that weak Armendariz rings are quasi-regular Armendariz rings,and direct products∏i∈I R i is a quasi-regular Armendariz ring if and only if each R i(i∈I)is a quasi-regular Armendariz ring.It is also proved that R is quasi-regular Armendariz ring if and only if the upper triangular matrix ring T n(R)(n≥2)is a quasi-regular Armendariz ring,and an example is given to illustrate that the full matrix ring M n(R)(n≥2)on any ring R is not a quasi-regular Armendariz ring.

关 键 词：拟正则元 弱ARMENDARIZ环 拟正则Armendariz环 半交换环 直积 上三角矩阵环 

分 类 号：O153.3[理学—数学]