Chain conditions for Leavitt path algebras

Chain conditions for Leavitt path algebras
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莱维特路径代数的链条件

DOI：
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发表时间：
2009
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通讯作者：
Mercedes Siles Molina
Mercedes Siles Molina
中科院分区：
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文献类型：
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作者：
G. Abrams;G. A. Pino;F. Perera;Mercedes Siles Molina

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本文给出了行有限图E的Leavitt路K-代数LK（E）从局部和范畴两个角度都是Artinian或Noether的充要条件。这些结果将单位元情形下的已知结果推广到更广的范围。除了图论条件外，我们还在这两种情况下给出了这些代数之间的同构以及K或K[x，x-1]上矩阵环的直和.
Abstract In this paper we give necessary and sufficient conditions on a row-finite graph E so that the corresponding (not necessarily unital) Leavitt path K-algebra LK (E) is either artinian or noetherian from both a local and a categorical perspective. These extend the known results in the unital case to a much wider context. Besides the graph theoretic conditions, we provide in both situations isomorphisms between these algebras and appropriate direct sums of matrix rings over K or K[x, x –1].