You mention in your proposed tag-excerpt that other uses of "ideal" are closely related to the ring-theoretic one. The only reason I can see in restricting the ideals tag to the ring-theoretic sense, while leaving the filters tag open to various related notions, is the coincidence of how it is currently being used. I'm not certain if this is a good enough reason. The fact that questions may be (and usually should be) given multiple tags to help someone browsing decide whether a question is of interest strengthens, IMHO, my claim that the scope of ideals should not be restricted. — Arthur Fischer ♦ Jul 31 '12 at 9:30