  In this article, we provide an explicit description of a set of generators
for any ideal of an ultragraph Leavitt path algebra. We provide several
additional consequences of this description, including information about
generating sets for graded ideals, the graded uniqueness and Cuntz-Krieger
theorems, the semiprimeness, and the semiprimitivity of ultragraph Leavitt path
algebras, a complete characterization of the prime and primitive ideals of an
ultragraph Leavitt path algebra. We also show that every primitive ideal of an
ultragraph Leavitt path algebra is exactly the annihilator of a Chen simple
module. Consequently, we prove Exel's Effros-Hahn conjecture on primitive
ideals in the ultragraph Leavitt path algebra setting (a conclusion that is
also new in the context of Leavitt path algebras of graphs).
