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Journal of the London Mathematical Society (1)

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ON THE EXISTENCE OF ELEMENTS OF NON-NILPOTENT FINITE CLOSED DESCENT IN COMMUTATIVE RADICAL FRÉCHET ALGEBRAS
M. K. KOPP
Journal:

Journal of the London Mathematical Society / Volume 70 / Issue 1 / August 2004

Published online by Cambridge University Press:

23 July 2004, pp. 261-272

Print publication:

August 2004
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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 $\mathbb{C}_{\omega_{1}}$.