University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Primitive Ideal Space of Ultragraph $C^*$-algebras1471583572910.22130/scma.2018.82725.404ENMostafaImanfarFaculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, 15914 Tehran, Iran.AbdolrasoulPourabbasFaculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, 15914 Tehran, Iran.HosseinLarkiDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Iran.Journal Article20180306In 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.https://scma.maragheh.ac.ir/article_35729_73ba5420990970a0ddcac2ce5d817221.pdf