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Generalizations of a theorem of Mutylin


Author: Seth Warner
Journal: Proc. Amer. Math. Soc. 78 (1980), 327-330
MSC: Primary 12J99
DOI: https://doi.org/10.1090/S0002-9939-1980-0553369-9
MathSciNet review: 553369
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Abstract: We generalize Mutylin's theorem that the only complete, locally bounded, additively generated topological fields are R and C by showing: (1) the only complete, locally bounded, additively generated topological division rings with left bounded commutator subgroup are R, C, and H; (2) a commutative, Hausdorff topological ring A with identity is a Banach algebra over R, equipped with the absolute value $ \vert..{\vert^p}$ for some $ p \in (0,1]$, if (and only if) A is complete, locally bounded, additively generated, and possesses an invertible topological nilpotent.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0553369-9
Article copyright: © Copyright 1980 American Mathematical Society

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