A McCoy condition on noncommutative rings
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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.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.
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Key words:
- right McCoy ring /
- left McCoy ring /
- McCoy ring /
- matrix ring /
- upper triangular matrix ring
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[1] {1} NIELSEN P P. Semi-commutativity and the McCoy condition[J]. J Algebra, 2006, 298: 134-141.{2} MCCOY N H. Remaks on divisors of zero[J]. Amer Math Monthly, 1942, 49:286-295.{3} ZHENG L, JIAN L C, ZHI L Y. A question on McCoy rings[J]. Austral Math Soc, 2007, 76: 137-141.{4} YING Z L, CHEN J L, LEI Z. Extensions of McCoy rings[J]. Northeasters Mathematical J, 2008, 24(1): 85-94.{5} CAMILLO V, NIELSEN P P. McCoy rings and zero-divisors[J], J Pure and Applied Algebra, 2008, 212: 599-615.{6} CHAN YONG HONG, YOUNG CHEOL JEON, NAM KYUN KIM, et al. The McCoy condition on noncommutative rings[J]. Comm Algebra, 2011, 39: 1809-1825. -
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