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Annihilator topological algebras. (English) Zbl 0806.46051
Summary: We study annihilator topological algebras, not necessarily Banach or even locally convex ones, along with their structure theory. We also refer to \((D)\)-algebras, a convenient variant for \(Q\)-algebras. In fact, for semisimple annihilator algebras, \((D)\) and \(Q'\)-algebras coincide. Topological algebras with proper closed ideals having non-zero annihilators are also considered.

MSC:
46H05 General theory of topological algebras
46H10 Ideals and subalgebras
46H20 Structure, classification of topological algebras
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