华东师范大学学报(自然科学版) ›› 2013, Vol. 2013 ›› Issue (6): 74-82.

• 应用数学与基础数学 • 上一篇    下一篇

非交换环上的~McCoy~条件

王文康1,2   

  1. 1. 伊犁师范学院 数学与统计学院, 新疆 伊宁 835000; 2. 西北民族大学 数学与计算机科学学院, 兰州 730124
  • 收稿日期:2012-10-01 修回日期:2013-02-01 出版日期:2013-11-25 发布日期:2014-01-13

A McCoy condition on noncommutative rings

WANG Wen-kang1,2   

  1. 1. College of Mathematics and Statistics, Yili normal University, Yining Xinjiang 835000, China;
    2. School of mathematics and computer science, Northwest University for Nationalities, Lanzhou 730124, China
  • Received:2012-10-01 Revised:2013-02-01 Online:2013-11-25 Published:2014-01-13

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摘要： 在左(或右)~McCoy~环上的矩阵环和上三角矩阵环中,
找到了一些左(或右)~McCoy~子环;
同时给出了没有单位元的左(或右)~McCoy~环.
说明了一个左~McCoy~环不一定是右~McCoy~环,
一个右~McCoy~环不一定是左~McCoy~环.
最后指出~reversible~环满足一个~McCoy~条件.

关键词: 右~McCoy~环, 左McCoy~环, McCoy~环, 矩阵环, 上三角矩阵环

Abstract: Some right (resp., left) McCoy  subrings of matrix ring
and upper triangular matrix ring over a right (resp., left) McCoy
ring are presented. At the same time, we also give that  a right
McCoy ring is not left McCoy and  a left   McCoy ring is not right
McCoy. Consequently, reversible  rings satisfy a McCoy condition.

Key words: right McCoy ring, left McCoy ring, McCoy ring, matrix ring, upper triangular matrix ring

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