## Intersection of ideals in C*-algebra or even rings in general [closed]

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Intersection of ideals in C*-algebra or even rings in general

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 and J be a two sided closed ideal in the same C*-algebra. 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.