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On some Gelfand-Mazur like theorems in Banach algebras

Published online by Cambridge University Press:  17 April 2009

V.K. Srinivasan
V.K. Srinivasan
Affiliation:
Department of Mathematics, University of Texas at El Paso, El Paso, Texas, USA.
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 20 , Issue 2 , April 1979 , pp. 211 - 215
Copyright
Copyright © Australian Mathematical Society 1979

References

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[5]Srinivasan, V.K. and Shaing, Hu, “Algebraic conditions in Banach algebras”, submitted. See also the abstract, “Banach algebras and Bezout domains”, 78T-B180 in Notices Amer. Math. Soc. 25 (1978), A–590.Google Scholar