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ON THE EXISTENCE OF ELEMENTS OF NON-NILPOTENT FINITE CLOSED DESCENT IN COMMUTATIVE RADICAL FRÉCHET ALGEBRAS

Published online by Cambridge University Press:  23 July 2004

M. K. KOPP
M. K. KOPP
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, United [email protected]
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Abstract

It is established that in a commutative radical Fréchet algebra, elements of non-nilpotent finite closed descent exist if a locally non-nilpotent element of locally finite closed descent exists. Thus if $\mathbb{C}[[X]]$ can be embedded into the unitization of the algebra in such a way that $X$ is mapped to an element which is locally non-nilpotent, then it is possible to embed the ‘structurally rich’ algebra $\mathbb{C}_{\omega_{1}}$.

Keywords

46H40 (primary)46J0546M40 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 70 , Issue 1 , August 2004 , pp. 261 - 272
Copyright
The London Mathematical Society 2004

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