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A theorem in Banach algebras and its applications

Published online by Cambridge University Press:  17 April 2009

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

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If A is a complex Banach algebra which is also a Bezout domain, it is shown that for any prime p and a non-negative integer n, pn is not a topological divisor of zero. Using the above result it is shown that a complex Banach algebra which is a principal ideal domain is isomorphic to the complex field.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 20 , Issue 2 , April 1979 , pp. 247 - 252
Copyright
Copyright © Australian Mathematical Society 1979

References

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