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The weak density of the non-invertible elements of a commutative algebra

Published online by Cambridge University Press:  17 April 2009

L. Narici ,
G. Bachman  and
E. Beckenstein
L. Narici
Affiliation:
St John's University, Jamaica. New York, USA
G. Bachman
Affiliation:
Polytechnic Institute of Brooklyn, Brooklyn, New York, USA
E. Beckenstein
Affiliation:
Polytechnic Institute of Brooklyn, Brooklyn, New York, USA.
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Abstract

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Let X be a commutative locally convex Hausdorff topological algebra with identity over a non-trivially valued field F. Let Mc denote the continuous nontrivial homomorphisms of X into F and M the set of all maximal ideals of X. If the spectrum of each element x in X is the set of scalars {f(x) | f ∈ Mc}, it is shown that the singular elements of X are weakly dense in X if and only if M is an infinite set.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 3 , December 1971 , pp. 387 - 390
Copyright
Copyright © Australian Mathematical Society 1971

References

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