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A theorem in Banach algebras and its applications
Published online by Cambridge University Press: 17 April 2009
Abstract
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.
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- Copyright © Australian Mathematical Society 1979
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