| 拟-Armendariz模 |
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| 引用本文： | 张翠萍,陈建龙.拟-Armendariz模[J].数学研究及应用,2010,30(4):734-742. |
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| 作者姓名： | 张翠萍 陈建龙 |
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| 作者单位： | 西北师范大学数学系，甘肃 兰州 730070;东南大学数学系, 江苏\ 南京 210096 |
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| 基金项目： | 国家自然科学基金(Grant No.10571026), 高等学校博士点基金(Grant No.20060286006),西北师范大学青年教师科研基金项目(Grant No.NWNU-LKQN-08-1). |
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| 摘 要： | For a right R-module N, we introduce the quasi-Armendariz modules which are a common generalization of the Armendariz modules and the quasi-Armendariz rings, and investigate their properties. Moreover, we prove that NR is quasi-Armendariz if and only if Mm(N)Mm(R) is quasi-Armendariz if and only if Tm(N)Tm(R) is quasi-Armendariz, where Mm(N) and Tm(N) denote the m×m full matrix and the m×m upper triangular matrix over N, respectively. NR is quasi-Armendariz if and only if Nx]Rx] is quasi-Armendariz. It is shown that every quasi-Baer module is quasi-Armendariz module.
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| 关 键 词： | Armendariz modules quasi-Armendariz rings quasi-Armendariz modules quasiBaer modules. |
| 收稿时间： | 2008/6/12 0:00:00 |
| 修稿时间： | 2008/10/8 0:00:00 |
Quasi-Armendariz Modules |
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| Cui Ping ZHANG and Jian Long CHEN.Quasi-Armendariz Modules[J].Journal of Mathematical Research with Applications,2010,30(4):734-742. |
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| Authors: | Cui Ping ZHANG and Jian Long CHEN |
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| Institution: | 1. Department of Mathematics,Northwest Normal University,Gansu 730070,P.R.China
2. Department of Mathematics,Southeast University,Jiangsu 210096,P.R.China |
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| Abstract: | For a right $R$-module $N$, we introduce the quasi-Armendariz modules which are a common generalization of the Armendariz modules and the quasi-Armendariz rings, and investigate their properties. Moreover, we prove that $N_R$ is quasi-Armendariz if and only if $M_m(N)_{M_m(R)}$ is quasi-Armendariz if and only if $T_m(N)_{T_m(R)}$ is quasi-Armendariz, where $M_m(N)$ and $T_m(N)$ denote the $m\times m$ full matrix and the $m\times m$ upper triangular matrix over $N$, respectively. $N_R$ is quasi-Armendariz if and only if $Nx]_{Rx]}$ is quasi-Armendariz. It is shown that every quasi-Baer module is quasi-Armendariz module. |
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| Keywords: | Armendariz modules quasi-Armendariz rings quasi-Armendariz modules quasi-Baer modules |
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