Two-Sided Ideals in Leavitt Path Algebras

Details Two-Sided Ideals in Leavitt Path Algebras Two-Sided Ideals in Leavitt Path Algebras

2009-10-01

arxiv.org/abs/0910.0292v3

Mathematics

Rings and Algebras

9 pages, 1 figure

Scientific paper

We explicitly describe two-sided ideals in Leavitt path algebras associated with a row-finite graph. Our main result is that any two-sided ideal $I$ of a Leavitt path algebra associated with a row-finite graph is generated by elements of the form $v + \sum_{i=1}^n\lambda_i g^i$, where $g$ is a cycle based at vertex $v$. We use this result to show that a Leavitt path algebra is two-sided Noetherian if and only if the ascending chain condition holds for hereditary and saturated closures of the subsets of the vertices of the row-finite graph $E$.

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