Prime and Primitive Ideals of Ultragraph Leavitt Path Algebras

Abstract

Let G be an ultragraph and let K be a field. We describe prime and primitive ideals in the ultragraph Leavitt path algebra LK (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 LK (G) are always primitive.