Journal of Commutative Algebra

A theorem of Gilmer and the canonical universal splitting ring

Fred Richman

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We give a constructive proof of Gilmer's theorem that if every nonzero polynomial over a field $k$ has a root in some fixed extension field $E$, then each polynomial in $k[X]$ splits in $E[X]$. Using a slight generalization of this theorem, we construct, in a functorial way, a commutative, discrete, von Neumann regular $k$-algebra $A$ so that each polynomial in $k[X]$ splits in $A[X]$.

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J. Commut. Algebra, Volume 6, Number 1 (2014), 101-108.

First available in Project Euclid: 2 June 2014

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Richman, Fred. A theorem of Gilmer and the canonical universal splitting ring. J. Commut. Algebra 6 (2014), no. 1, 101--108. doi:10.1216/JCA-2014-6-1-101.

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