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A question on McCoy rings

Published online by Cambridge University Press:  17 April 2009

Zhen Lei ,
Jianlong Chen  and
Zhiling Ying
Zhen Lei
Affiliation:
Department of Mathematics, Anhui Normal University, Wuhu 241000, Peoples Republic of China, e-mail: [email protected]
Jianlong Chen
Affiliation:
Department of Mathematics, Southeast University, Nanjing 210096, Peoples Republic of China, e-mail: [email protected], e-mail: [email protected]
Zhiling Ying
Affiliation:
Department of Mathematics, Southeast University, Nanjing 210096, Peoples Republic of China, e-mail: [email protected], e-mail: [email protected]
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Nelsen [J. Algebra 298 (2006) 134–141] asked whether there is a natural class of McCoy rings which includes all reversible rings and all rings R such that R[X] is semi-commutative. In this paper, some new equivalent conditions of McCoy rings are given. One of them is used to answer this question in the affirmative. Finally, an example is given which is McCoy and semi-commutative, but it is not reversible and does not have the property that R[x] is semi-commutative.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 76 , Issue 1 , August 2007 , pp. 137 - 141
Copyright
Copyright © Australian Mathematical Society 2007

References

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[4]Nielsen, P.P., ‘Semi-commutativity and the McCoy condition’, J. Algebra 298 (2006), 134–141.CrossRefGoogle Scholar