Purely Infinite Simple Ultragraph Leavitt Path Algebras

In this article, we give necessary and sufficient conditions under which the Leavitt path algebra $$L_K(\mathcal {G})$$ of an ultragraph $$\mathcal {G}$$ over a field K is purely infinite simple that it von Neumann regular. Consequently, obtain every graded either locally matricial algebra, or full matrix ring $$K[x, x^{-1}]$$ , algebra.