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On Gelfand-Mazur theorem on a class of \(F\)-algebras. (English) Zbl 1316.46040

The paper generalizes the Gelfand-Mazur theorem for a special class of \(F\)-algebras: fundamental division \(F\)-algebras with bounded elements and with dual of the algebra separating the points of algebra. It is shown that in this case the algebra under consideration is isomorphic to the field of complex numbers. As an addition, some examples of non-locally bounded \(F\)-algebras and non-locally convex \(F\)-algebras belonging to that class of \(F\)-algebras are given. It is also shown that the spectrum of an arbitrary element of a fundamental \(F\)-algebra whose dual separates its points is a nonempty compact set.
Reviewer: Mart Abel (Tartu)

MSC:

46H05 General theory of topological algebras
46H20 Structure, classification of topological algebras
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References:

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