Kar-Ping Shum

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Denote the 2×2 upper triangular matrix rings over Z and Z p by UTM 2 (Z) and UTM 2 (Z 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 UTM 2 (Z) or UTM 2 (Z p). Other conditions for a p.p.-ring to be reduced are also given. Our results strengthen and extend the results(More)