Abstract

Denote the 2×2 upper triangular matrix rings over and p by UTM2() and UTM2(p), 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() or UTM2(p). 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.