| 一类替换环的偏序$K_{0}$-群的无扭性 |
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| 引用本文： | 吴阔华,吕新民.一类替换环的偏序$K_{0}$-群的无扭性[J].数学研究及应用,2009,29(2):367-370. |
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| 作者姓名： | 吴阔华 吕新民 |
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| 作者单位： | 江西理工大学理学院,江西 赣州 341000;江西理工大学理学院,江西 赣州 341000 |
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| 基金项目： | 国家自然科学基金(No.10571080);江西省自然科学基金(No.0611042);江西省科学技术计划项目(G[2006]194). |
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| 摘 要： | A ring R is called orthogonal if for any two idempotents e and f in R, the condition that e and f are orthogonal in R implies the condition that eR] and fR] are orthogonal in K0（R）^＋, i.e., eR]∧fR] = 0. In this paper, we shall prove that the K0-group of every orthogonal, IBN2 exchange ring is always torsion-free, which generalizes the main result in 3].
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| 关 键 词： | 替换环 偏序Ko群 无扭性 IBN2环 正交环 |
| 收稿时间： | 2/7/2007 12:00:00 AM |
| 修稿时间： | 2007/7/13 0:00:00 |
The Torsion-Freeness of Partially Ordered $K_{0}$-Groups for a Class of Exchange Rings |
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| WU Kuo Hua and L\"{U} Xin Min.The Torsion-Freeness of Partially Ordered $K_{0}$-Groups for a Class of Exchange Rings[J].Journal of Mathematical Research with Applications,2009,29(2):367-370. |
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| Authors: | WU Kuo Hua and L\"{U} Xin Min |
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| Institution: | Faculty of Science, Jiangxi University of Science and Technology, Jiangxi 341000, China;Faculty of Science, Jiangxi University of Science and Technology, Jiangxi 341000, China |
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| Abstract: | A ring $R$ is called orthogonal if for any two idempotents $e$ and $f$ in $R$, the condition that $e$ and $f$ are orthogonal in $R$ implies the condition that $eR]$ and $fR]$ are orthogonal in $K_{0}(R)^{+}$, i.e., $eR]\wedge fR]=0$. In this paper, we shall prove that the $K_{0}$-group of every orthogonal, $IBN_{2}$ exchange ring is always torsion-free, which generalizes the main result in 3]. |
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| Keywords: | $IBN_{2}$ ring Orthogonal ring $K_{0}$-group Partially ordered Abelian group $\ell$-group |
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