Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-06-25T23:34:20.998Z Has data issue: false hasContentIssue false
  • English
  • Français

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: wuhuleizhen@126.com
Jianlong Chen
Affiliation:
Department of Mathematics, Southeast University, Nanjing 210096, Peoples Republic of China, e-mail: jlchen@seu.edu.cn, e-mail: zhilingying@Yahoo.com.cn
Zhiling Ying
Affiliation:
Department of Mathematics, Southeast University, Nanjing 210096, Peoples Republic of China, e-mail: jlchen@seu.edu.cn, e-mail: zhilingying@Yahoo.com.cn
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Anderson, D.D. and Camillo, V., ‘Armendariz rings and Gaussian rings’, Comm. Algebra 26 (1998), 2265–2272.CrossRefGoogle Scholar
[2]Hirano, Y., ‘On annihilator ideals of a polynomial ring over a noncommutative ring’, J. Pure Appl. Algebra 168 (2002), 45–52.CrossRefGoogle Scholar
[3]Huh, C., Lee, Y. and Smoktunowicz, A., ‘Armendariz rings and semicommutative rings’, Comm. Algebra 30 (2002), 751–761.CrossRefGoogle Scholar
[4]Nielsen, P.P., ‘Semi-commutativity and the McCoy condition’, J. Algebra 298 (2006), 134–141.CrossRefGoogle Scholar