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On some Gelfand-Mazur like theorems in Banach algebras
Published online by Cambridge University Press: 17 April 2009
Abstract
The following Gelfand-Mazur like theorems are proved in this paper:
(1) A complex Banach algebra which is locally finite, and which is also an integral domain, is isomorphic to the complex field .
(2) A complex Banach algebra which is a noetherian domain is isomorphic to .
(3) A complex Banach algebra which is a principal ideal domain is isomorphic to .
An application is given to the algebra of all complex formal power series in several variables.
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- Copyright © Australian Mathematical Society 1979
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