Dear all, here is a question that has been bothering me. It goes without saying that I would appreciate any help in answering it.

Let {I_k} be a countable sequence of two sided closed ideals in a C*-algebra (ring) and J be a two sided closed ideal in the same C*-algebra (ring). Then "intersection of {I_k + J} = (intersection of {I_k}) + J"

If needed we can relax the above hypothesis by assuming that {I_k}'s and J are prime ideals.

Thanks in advance, Audrey Kirilova.