A McCoy condition on noncommutative rings

WANG Wen-kang

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WANG Wen-kang. A McCoy condition on noncommutative rings[J]. Journal of East China Normal University (Natural Sciences), 2013, (6): 74-82.

Citation:

WANG Wen-kang. A McCoy condition on noncommutative rings[J]. Journal of East China Normal University (Natural Sciences), 2013, (6): 74-82.

WANG Wen-kang. A McCoy condition on noncommutative rings[J]. Journal of East China Normal University (Natural Sciences), 2013, (6): 74-82.

Citation:

WANG Wen-kang. A McCoy condition on noncommutative rings[J]. Journal of East China Normal University (Natural Sciences), 2013, (6): 74-82.

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A McCoy condition on noncommutative rings

WANG Wen-kang^1,2

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 Date: 2012-10-01
Rev Recd Date: 2013-02-01
Publish Date: 2013-11-25

Abstract

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.
- right McCoy ring,
- left McCoy ring,
- McCoy ring,
- matrix ring,
- upper triangular matrix ring

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References(1)

References

[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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