Generalizations of a theorem of Mutylin

Warner, Seth

doi:10.1090/S0002-9939-1980-0553369-9

Generalizations of a theorem of Mutylin
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Proc. Amer. Math. Soc. 78 (1980), 327-330 Request permission

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 $|..{|^p}$ 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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Topologie générale

Algèbre commutative

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