TWO-SIDED CHAIN CONDITIONS IN LEAVITT PATH ALGEBRAS OVER ARBITRARY GRAPHS

TWO-SIDED CHAIN CONDITIONS IN LEAVITT PATH ALGEBRAS OVER ARBITRARY GRAPHS
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任意图上莱维特路径代数的双边链条件

DOI：
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发表时间：
2012
期刊：
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通讯作者：
K. Rangaswamy
K. Rangaswamy
中科院分区：
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文献类型：
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作者：
G. Abrams;J. Bell;Pınar Çolak;K. Rangaswamy

文献摘要

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设E是任意有向图，K是任意域。对于Leavitt路代数LK（E）的任意理想I，我们给出了I的生成元集的显式描述。这种描述使我们能够对任意图上的双侧诺特莱维特路代数进行分类。这扩展了以前只在行有限的情况下已知的类似结果。我们提供了一些额外的后果，这种描述，包括识别的莱维特路代数，所有的双边理想是分等级的。最后，我们对任意图上的双边artinian Leavitt路代数进行了分类。
Let E be any directed graph, and K be any field. For any ideal I of the Leavitt path algebra LK(E) we provide an explicit description of a set of generators for I. This description allows us to classify the two-sided noetherian Leavitt path algebras over arbitrary graphs. This extends similar results previously known only in the row-finite case. We provide a number of additional consequences of this description, including an identification of those Leavitt path algebras for which all two-sided ideals are graded. Finally, we classify the two-sided artinian Leavitt path algebras over arbitrary graphs.