Intersection of ideals in C*-algebra or even rings in general - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-19T08:51:41Z http://mathoverflow.net/feeds/question/26479 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/26479/intersection-of-ideals-in-c-algebra-or-even-rings-in-general Intersection of ideals in C*-algebra or even rings in general Audrey Kirilova 2010-05-30T18:14:45Z 2010-05-30T18:14:45Z <blockquote> <p><strong>Possible Duplicate:</strong><br> <a href="http://mathoverflow.net/questions/26482/intersection-of-ideals-in-c-algebra-or-even-rings-in-general" rel="nofollow">Intersection of ideals in C*-algebra or even rings in general </a> </p> </blockquote> <p>Dear all, here is a question that has been bothering me. It goes without saying that I would appreciate any help in answering it.</p> <p>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" </p> <p>If needed we can relax the above hypothesis by assuming that {I_k}'s and J are prime ideals.</p> <p>Thanks in advance, Audrey Kirilova. </p>