International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 4, Pages 34694, 5 p.
doi:10.1155/IJMMS/2006/34694
On p.p.-rings which are reduced.
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
Abstract
Denote the 2×2 upper triangular matrix rings over ℤ and ℤp by UTM2(ℤ) and UTM2(ℤp), respectively. We prove that if a ring R is a p.p.-ring, then R is reduced if and only if R does not contain any subrings isomorphic to UTM2(ℤ) or UTM2(ℤp). 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.