T-幂零环的若干扩张  

Some extensions of T-nilpotent rings

作　　者：马广琳 王尧[1] 任艳丽[2] MA Guang-lin;WANG Yao;REN Yan-li(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,Jiangsu,China;School of Information Engineering,Nanjing Xiaozhuang University,Nanjing 211171,Jiangsu,China)

机构地区：[1]南京信息工程大学数学与统计学院,江苏南京210044 [2]南京晓庄学院信息工程学院,江苏南京211171

出　　处：《山东大学学报（理学版）》2019年第12期68-73,共6页Journal of Shandong University(Natural Science)

基　　金：江苏省自然科学基金资助项目(BK20181406)

摘　　要：研究T-幂零环的一些扩张性质,主要证明了:(1)设R是一个环,α是R上的自同构,则R是左T-幂零环当且仅当R上的斜多项式环R[x;α]是左T-幂零环,当且仅当斜洛朗多项式环R[x,x-1;α]是左T-幂零环;(2)环R是左T-幂零环当且仅当R上的Nagata扩张是左T-幂零环,当且仅当R上的斜三角矩阵环是左T-幂零环。Some extension properties of T-nilpotent rings are investigated. It is mainly proved that(1) If R is a ring and α an automorphism of R, then R is a left T-nilpotent ring if and only if the skew polynomial ring R[x;α] over R is a left T-nilpotent ring, if and only if the skew Laurent polynomial ring R[x,x-1;α] is a left T-nilpotent ring;(2) R is a left T-nilpotent ring if and only if the Nagata extension over R is a left T-nilpotent ring, if and only if the skew triangular matrix ring over R is a left T-nilpotent ring.

关 键 词：T-幂零环 斜多项式环 斜洛朗多项式环 Nagata扩张 斜三角矩阵环 

分 类 号：O153.3[理学—数学]