Quasi-duo rings and stable range descent
Quasi-duo rings and stable range descent
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DOI：
10.1016/j.jpaa.2004.08.011
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发表时间：
2005-02
影响因子：
0.8
通讯作者：
T. Lam;A. Dugas
中科院分区：
文献类型：
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作者：
T. Lam;A. Dugas
在最近的一篇论文中，第一作者介绍了非交换环中角环的一般理论，推广了经典的Peirce分解理论。这个理论在这里应用于研究下降到角环的稳定范围。一个环称为拟duo，如果每个极大单侧理想都是双侧的。得到了这类环的各种新的刻画。利用其中的一些刻画，我们证明了：若拟duo环R有稳定值域n，则R的任何半分裂角环也是如此.这与Vaserstein和沃菲尔德的早期结果形成对比，后者表明稳定范围可以在下降到（甚至）皮尔士角环时无限增加。
In a recent paper, the first author introduced a general theory of corner rings in noncommutative rings that generalized the classical theory of Peirce decompositions. This theory is applied here to the study of the stable range of rings upon descent to corner rings. A ring is called quasi-duo if every maximal 1-sided ideal is 2-sided. Various new characterizations are obtained for such rings. Using some of these characterizations, we prove that, if a quasi-duo ring R has stable range ⩽n, the same is true for any semisplit corner ring of R. This contrasts with earlier results of Vaserstein and Warfield, which showed that the stable range can increase unboundedly upon descent to (even) Peirce corner rings.