Prime and Primitive Ideals of Ultragraph Leavitt Path Algebras
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 nongraded prime ideals. We show that the nongraded prime ideals of $L_K(\mathcal G)$ are always primitive.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.12011
 Bibcode:
 2021arXiv210912011P
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  Operator Algebras