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arXiv · 1307.4662

Radical Extensions for the Carlitz--Hayes Module

Marco Sánchez--Mirafuentes·Gabriel Villa--Salvador
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Abstract

Let $L/K$ be a finite extension of congruence function fields. We say that $L/K$ is a {\it radical extension} if $L$ is generated by roots of polynomials $u^{M}-α\in K[u]$, where $u^{M}$ is the action of Carlitz-Hayes. We study a special class of these extensions, the {\it radical cyclotomic} extensions. We prove that any radical cyclotomic extension has order a power of the characteristic of $K$. We also give bounds for the Carlitz-Hayes torsion of these extensions.

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Marco Sánchez--Mirafuentes, Gabriel Villa--Salvador. 2013-07-17. Radical Extensions for the Carlitz--Hayes Module. https://arxiv.org/abs/1307.4662

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