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 non-graded prime ideals. We show that the non-graded prime ideals of $L_K(\mathcal{G})$ are always primitive.

References in corpus (2)

• Morita Equivalence of Graph and Ultragraph Leavitt Path Algebras
• Realizing ultragraph Leavitt path algebras as Steinberg algebras