On Semiabelian π -Regular Rings

Weixing Chen

International Journal of Mathematics and Mathematical Sciences, 2007, vol. 2007, 1-10

Abstract:

A ring R is defined to be semiabelian if every idempotent of R is either right semicentral or left semicentral. It is proved that the set N ( R ) of nilpotent elements in a π -regular ring R is an ideal of R if and only if R / J ( R ) is abelian, where J ( R ) is the Jacobson radical of R . It follows that a semiabelian ring R is π -regular if and only if N ( R ) is an ideal of R and R / N ( R ) is regular, which extends the fundamental result of Badawi (1997). Moreover, several related results and examples are given.

Date: 2007
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2007/063171.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2007/063171.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:063171

DOI: 10.1155/2007/63171

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().