Centers of $C^{\ast }$-algebras rich in modular ideals

Abstract

We provide, in the spirit of a 1968 paper of C. Delaroche, new conditions under which a $C^{\ast }$-algebra has a nonzero center.We also present an example of a (separable) AF algebra with center $\{0\}$ but whose all the primitive ideals are modular, thus answering a question from that paper of Delaroche.

5 pages, one figure. The main result in the previous version has been generalized and new results have been added