ideal of an non-nuclear $C^*$ algebra

Question

If $A$ is a nuclear $C^*$-algebra,$I$ is a closed ideal of $A$,then $A/I$ is nuclear.

My question :Does there exist an non-nuclear $C^*$-algebra whose quotient is nuclear?

Answer 1

Of course. Take $A$ nuclear, $B$ non-nuclear, and consider $A\oplus B$. With $I=0\oplus B$, you have $(A\oplus B)/I\simeq A$.