On p.p.-rings which are reduced

Xiaojiang Guo and K. P. Shum

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-5

Abstract:

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 of Fraser and Nicholson on r.p.p.-rings.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:034694

DOI: 10.1155/IJMMS/2006/34694

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