%0 Journal Article %T Primitive Ideal Space of Ultragraph $C^*$-algebras %J Sahand Communications in Mathematical Analysis %I University of Maragheh %Z 2322-5807 %A Imanfar, Mostafa %A Pourabbas, Abdolrasoul %A Larki, Hossein %D 2019 %\ 07/01/2019 %V 15 %N 1 %P 147-158 %! Primitive Ideal Space of Ultragraph $C^*$-algebras %K Ultragraph %K Ultragraph $C^*$-algebra %K Primitive ideal %R 10.22130/scma.2018.82725.404 %X 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 gauge-invariant 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. %U https://scma.maragheh.ac.ir/article_35729_73ba5420990970a0ddcac2ce5d817221.pdf