Given a C*-algebra without unit.
Does there exist a nontrivial proper ideal
that does not lie in a maximally nontrivial proper ideal?
(For the unital case this follows easily by Zorn's lemma.)
Whatwould be an example of such?
Given a C*-algebra without unit.
Does there exist a nontrivial proper ideal
that does not lie in a maximally nontrivial proper ideal?
(For the unital case this follows easily by Zorn's lemma.)
Whatwould be an example of such?
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