| The Torsion-Freeness of Partially Ordered $K_{0}$-Groups for a Class of Exchange Rings |
| Received:February 07, 2007 Revised:July 13, 2007 |
| Key Words:
$IBN_{2}$ ring Orthogonal ring $K_{0}$-group Partially ordered Abelian group $\ell$-group.
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| Fund Project:the National Natural Science Foundation of China (No.\,10571080); the Natural Science Foundation of Jiangxi Province (No.\,0611042); the Science and Technology Projiet Foundation of Jiangxi Province (No.\,G[2006]194) and the Doctor Foundation of Jiangxi U |
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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]. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2009.02.022 |
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