Armendariz and reduced rings

被引：82

作者：

Lee, TK

Zhou, YQ ^{[1
]}

机构：

[1] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

[2] Natl Taiwan Univ, Dept Math, Taipei, Taiwan

来源：

COMMUNICATIONS IN ALGEBRA | 2004年 / 32卷 / 06期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Armendariz ring; matrix ring; reduced ring; trivial extension;

D O I：

10.1081/AGB-120037221

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A ring R is called Armendariz if, whenever (Sigma(i=0)(s) a(i)x(i))(Sigma(j=0)(t)b(j)x(j)) = 0 in R[x], a(i)b(j) = 0 for all i and j. In this paper, some "relatively maximal" Armendariz subrings of matrix rings are identified, and a necessary and sufficient condition for a trivial extension to be Armendariz is obtained. Consequently, new families of Armendariz rings are presented.

引用

页码：2287 / 2299

页数：13

共 11 条

[1] Armendariz rings and Gaussian rings [J].