Primitive Ideal Space of Ultragraph $C^*$algebras

In this paper, we describe the primitive ideal space of the $C^*$algebra $C^*(mathcal G)$  associated to the ultragraph $mathcal{G}$. We investigate the structure of the closed ideals of the quotient ultragraph $  C^* $algebra  $C^*left(mathcal G/(H,S)right)$ which contain no nonzero set projections and then we characterize all non gaugeinvariant primitive ideals. Our results generalize the Hong and Szyma$ acute{ mathrm { n } } $ski’s description of the primitive ideal space of a graph $ C ^ * $algebra by a simpler method.