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arXiv · 1709.01582

Chain conditions on étale groupoid algebras with applications to Leavitt path algebras and inverse semigroup algebras

Benjamin Steinberg
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Abstract

The author has previously associated to each commutative ring with unit $R$ and étale groupoid $\mathscr G$ with locally compact, Hausdorff and totally disconnected unit space an $R$-algebra $R\mathscr G$. In this paper we characterize when $R\mathscr G$ is Noetherian and when it is Artinian. As corollaries, we extend the characterization of Abrams, Aranda~Pino and Siles~Molina of finite dimensional and of Noetherian Leavitt path algebras over a field to arbitrary commutative coefficient rings and we recover the characterization of Okniński of Noetherian inverse semigroup algebras and of Zelmanov of Artinian inverse semigroup algebras.

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Benjamin Steinberg. 2017-09-09. Chain conditions on étale groupoid algebras with applications to Leavitt path algebras and inverse semigroup algebras. https://arxiv.org/abs/1709.01582

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