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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
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 $\mathbb{C}_{\omega_{1}}$.
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- The London Mathematical Society 2004