一类上三角矩阵环的Armendariz与半交换性质  

Armendariz and semicommutative properties of a class of upper triangular matrix rings

作　　者：王文康[1] 

机构地区：[1]西北民族大学计算机科学与信息工程学院,甘肃兰州730124

出　　处：《山东大学学报（理学版）》2008年第2期62-65,共4页Journal of Shandong University(Natural Science)

摘　　要：称环R是Armendariz环,如果(∑mi=0aixi)(∑nj=0bjxj)=0∈R[x],那么aibj=0,其中0≤i≤m,0≤j≤n。称环R是reduced环,如果它没有非零的幂零元。称环R是半交换环,如果由ab=0,可得aRb=0,其中a,b∈R。找到了reduced环上的上三角矩阵环的一类子环既是Armendariz环又是半交换环。A ring R is called Armendariz, if （^m∑i=0 aix^i）（^n∑j=0 bjx^j）：0∈R[x], then aibj =0, where 0≤i≤m, 0≤j≤n. A ring R is called semicommutative if for any a, b∈R, ab = 0 implies aRb = 0. A ring is called reduced if it has no non-zero nilpotent elements. Every reduced ring is semicommutative. A class of upper triangular matrix rings over-reduced rings is found to be both Armendariz and semicommutative.

关 键 词：ARMENDARIZ环 REDUCED环 上三角矩阵环 半交换环 

分 类 号：O153.3[理学—数学]