| Some Characterizations of Pr\"{u}fer $v$-Multiplication Rings |
| Received:May 24, 2013 Revised:November 11, 2013 |
| Key Words:
$w$-ideal integrally closed PVMR complete.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11171240; 10971090) and the Scientific Research Fund of Sichuan Provincial Education Department (Grant Nos.14ZB0035; 12ZB107). |
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| Abstract: |
| In this paper, we study Pr\"{u}fer $v$-multiplication rings (PVMRs) and give some new characterizations of PVMRs. Moreover, we show that a Marot ring $R$ is a PVMR if and only if every $w$-ideal of $R$ is complete. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2014.03.005 |
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