| 关于w-linked扩环 |
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| 引用本文： | 谢林,王芳贵,田艳.关于w-linked扩环[J].数学研究与评论,2011,31(2):337-346. |
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| 作者姓名： | 谢林 王芳贵 田艳 |
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| 作者单位： | 四川师范大学数学与软件科学学院, 四川 成都 610068;四川师范大学数学与软件科学学院, 四川 成都 610068;四川师范大学数学与软件科学学院, 四川 成都 610068 |
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| 基金项目： | 国家自然科学基金(Grant No.10671137); 高等学校博士点基金(Grant No.20060636001). |
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| 摘 要： | Let R ■ T be an extension of commutative rings.T is called w-linked over R if T as an R-module is a w-module.In the case of R ■ T ■ Q 0 （R）,T is called a w-linked overring of R.As a generalization of Wang-McCsland-Park-Chang Theorem,we show that if R is a reduced ring,then R is a w-Noetherian ring with w-dim（R） 1 if and only if each w-linked overring T of R is a w-Noetherian ring with w-dim（T ） 1.In particular,R is a w-Noetherian ring with w-dim（R） = 0 if and only if R is an Artinian ring.
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| 关 键 词： | GV -ideal w-module w-linked w-Noetherian ring |
| 收稿时间： | 2009/1/12 0:00:00 |
| 修稿时间： | 2010/1/18 0:00:00 |
On $w$-Linked Overrings |
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| Lin XIE,Fang Gui WANG and Yan TIAN.On $w$-Linked Overrings[J].Journal of Mathematical Research and Exposition,2011,31(2):337-346. |
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| Authors: | Lin XIE Fang Gui WANG and Yan TIAN |
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| Institution: | Department of Mathematics, Sichuan Normal University, Sichuan $610068$, P. R. China;Department of Mathematics, Sichuan Normal University, Sichuan $610068$, P. R. China;Department of Mathematics, Sichuan Normal University, Sichuan $610068$, P. R. China |
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| Abstract: | Let $R\subseteq T$ be an extension of commutative rings. $T$ is called $w$-linked over $R$ if $T$ as an $R$-module is a $w$-module. In the case of $R\subseteq T\subseteq Q_0(R)$, $T$ is called a $w$-linked overring of $R$. As a generalization of Wang-McCsland-Park-Chang Theorem, we show that if $R$ is a reduced ring, then $R$ is a $w$-Noetherian ring with $w$-$\dim(R)\leqslant 1$ if and only if each $w$-linked overring $T$ of $R$ is a $w$-Noetherian ring with $w$-$\dim(T)\leqslant 1$. In particular, $R$ is a $w$-Noetherian ring with $w$-$\dim(R)=0$ if and only if $R$ is an Artinian ring. |
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| Keywords: | GV-ideal w-module w-linked w-Noetherian ring |
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