On p.p.-rings which are reduced
2006 ◽
Vol 2006
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pp. 1-5
Denote the2×2upper triangular matrix rings overℤandℤpbyUTM2(ℤ)andUTM2(ℤp), respectively. We prove that if a ringRis a p.p.-ring, thenRis reduced if and only ifRdoes not contain any subrings isomorphic toUTM2(ℤ)orUTM2(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.
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2017 ◽
Vol 91
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pp. 563-578
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Vol 426
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pp. 143-148
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pp. 263-267
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Vol 19
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pp. 2050053
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pp. 4622-4636
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