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 |
一类替换环的偏序$K_{0}$-群的无扭性 |
The Torsion-Freeness of Partially Ordered $K_{0}$-Groups for a Class of Exchange Rings |
投稿时间:2007-02-07 修订日期:2007-07-13 |
DOI:10.3770/j.issn:1000-341X.2009.02.022 |
中文关键词: $IBN_{2}$环 正交环 $K_{0}$-群 偏序Abel群 $\ell$-群. |
英文关键词:$IBN_{2}$ ring Orthogonal ring $K_{0}$-group Partially ordered Abelian group $\ell$-group. |
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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中文摘要: |
一个环$R$称为正交环,如果对于$R$的任意两个幂等元$e$和$f$, $e$和$f$在$R$中正交,即$ef=fe=0$, 蕴涵着$[eR]$和$[fR]$在$K_{0}(R)^{ }$中正交,即$[eR]\wedge [fR]=0$.本文我们将证明:每个正交的, $IBN_{2}$的替换环的$K_{0}$-群总是无扭的.这一结果推广了吕和秦在[3]中的主要结果. |
英文摘要: |
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 $K_{0}(R)^{ }$, 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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