On p.p.-rings which are reduced
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 gi...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/34694 |
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| Summary: | 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |