International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 92890, 7 pages

Reduced p.p.-rings without identity

Xiaojiang Guo1 and K. P. Shum2

1Department of Mathematics, Jiangxi Normal University, Nanchang, Jiangxi 330027, China
2Faculty of Science, The Chinese University of Hong Kong, Shatin, Hong Kong

Received 16 March 2006; Accepted 19 March 2006

Copyright © 2006 Xiaojiang Guo and K. P. Shum. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We give some necessary and sufficient conditions for p.p.-rings without identity to be reduced. Our results strengthen and extend the results of Fraser and Nicholson as well as some recent results we obtained on reduced p.p.-rings with identity.