张翠萍,陈建龙.拟-Armendariz模[J].数学研究及应用,2010,30(4):734~742 |
拟-Armendariz模 |
Quasi-Armendariz Modules |
投稿时间:2008-06-12 修订日期:2008-10-08 |
DOI:10.3770/j.issn:1000-341X.2010.04.018 |
中文关键词: Armendariz模 拟-Armendariz环 拟-Armendariz模 拟-Baer模. |
英文关键词:Armendariz modules quasi-Armendariz rings quasi-Armendariz modules quasi-Baer modules. |
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). |
|
摘要点击次数: 2523 |
全文下载次数: 2439 |
中文摘要: |
对于右$R$-模$N$,我们引入了拟-Armendariz模的概念,它是Armendariz模和拟-Armendariz环的共同推广,研究了它的性质.此外,我们证明了$N_R$是拟-Armendariz的当且仅当$M_m(N)_{M_m(R)}$是拟-Armendariz的当且仅当$T_m(N)_{T_m(R)}$是拟-Armendariz的,其中$M_m(N)$和$T_m(N)$分别表示$N$上的$m\times m$全矩阵和$m\times m$上三角矩阵.$N_R$是拟-Armendariz的当且仅当$N[x]_{R[x]}$是拟-Armendariz的.每个拟-Baer模是拟-Armendariz的. |
英文摘要: |
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 $N_R$ 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 $N[x]_{R[x]}$ is quasi-Armendariz. It is shown that every quasi-Baer module is quasi-Armendariz module. |
查看全文 查看/发表评论 下载PDF阅读器 |