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arXiv · 2109.12011

Prime and Primitive Ideals of Ultragraph Leavitt Path Algebras

A. Pourabbas·M. Imanfar·H. Larki
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Abstract

Let $\mathcal G$ be an ultragraph and let $K$ be a field. We describe prime and primitive ideals in the ultragraph Leavitt path algebra $L_K(\mathcal G)$. We identify the graded prime ideals in terms of downward directed sets and then we characterize the non-graded prime ideals. We show that the non-graded prime ideals of $L_K(\mathcal G)$ are always primitive.

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A. Pourabbas, M. Imanfar, H. Larki. 2021-09-24. Prime and Primitive Ideals of Ultragraph Leavitt Path Algebras. https://arxiv.org/abs/2109.12011

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