| 关于拟WGP-内射模 |
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| 引用本文： | 陈平,宋贤梅.关于拟WGP-内射模[J].安庆师范学院学报(自然科学版),2012,18(3):18-20,27. |
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| 作者姓名： | 陈平 宋贤梅 |
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| 作者单位： | 安徽师范大学数学与计算机科学学院,安徽芜湖,241000;安徽师范大学数学与计算机科学学院,安徽芜湖,241000 |
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| 基金项目： | 安徽省教育厅自然科学研究重点项目(KJ2010A126);安徽师范大学专项基金(2008xzx10)资助 |
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| 摘 要： | 定义了拟WGP-内射模,给出了拟WGP-内射模的一些刻画及性质。设R为环,M是右R-模,S=End(M),证明了MR是一个右拟WGP-内射模当且仅当对于任意的0≠a∈S,存在0≠c∈S,使得ac≠0且lS(ker(ac))=Sac;设M是右拟WGP-内射的自生成子,S半素,则S的每个极大核是M的直和项;设MR是右拟WGP-内射模,对于S的任意右一致元u,Au={s∈S|kers∩u(M)≠0}是包含ls(u(M))的一个极大左理想,从而推广了WGP-内射环的一些结果。
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| 关 键 词： | 拟WGP-内射模 WGP-内射环 自生成子 |
On Quasi WGP-injective Mdules |
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| CHEN Ping,SONG Xian-mei.On Quasi WGP-injective Mdules[J].Journal of Anqing Teachers College(Natural Science Edition),2012,18(3):18-20,27. |
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| Authors: | CHEN Ping SONG Xian-mei |
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| Institution: | (College of Mathematic and Computer Science,Anhui Normal University,Wuhu,Anhui 241000,China) |
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| Abstract: | Quasi WGP-injective modules are defined.Then some characterizations and properties are given.Let R be a ring,M right R-module,S=End(MR).It is shown that M is a right quasi WGP-injective module if and only if for and 0≠a∈S,there exists 0≠c∈S such that lS(ker(ac))=Sac.Moreover,it is proved that if M is a right quasi WGP-injective self-generator and S is a semiprime ring,then every maximal kernel of S is a summand of M;If M is a right quasi WGP-injective module,then for any right uniform element of S,the set Au={s∈S|kers∩u(M)≠0} is a maximal left ideal of S containing lS(u(M)).Consequently,some results of WGP-injective rings are generalized. |
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| Keywords: | quasi WGP-injective module WGP-injective ring self-generator |
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