International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 34694, 5 pages
On p.p.-rings which are reduced
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.
Denote the upper triangular matrix rings over
, respectively. We prove that if a ring
is a p.p.-ring, then is reduced if and only if does
not contain any subrings isomorphic to or
. Other conditions for a p.p.-ring to be
reduced are also given. Our results strengthen and extend the
results of Fraser and Nicholson on r.p.p.-rings.