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SPRING 2014 A theorem of Gilmer and the canonical universal splitting ring
Fred Richman
J. Commut. Algebra 6(1): 101-108 (SPRING 2014). DOI: 10.1216/JCA-2014-6-1-101

Abstract

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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Fred Richman. "A theorem of Gilmer and the canonical universal splitting ring." J. Commut. Algebra 6 (1) 101 - 108, SPRING 2014. https://doi.org/10.1216/JCA-2014-6-1-101

Information

Published: SPRING 2014
First available in Project Euclid: 2 June 2014

zbMATH: 1291.12001
MathSciNet: MR3215563
Digital Object Identifier: 10.1216/JCA-2014-6-1-101

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

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Vol.6 • No. 1 • SPRING 2014
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