Generic extensions and generic Polynomials for multiplicative groups

Jorge Morales; Anthony Sanchez

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arXiv · 1405.7807

Generic extensions and generic Polynomials for multiplicative groups

Jorge Morales·Anthony Sanchez

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Abstract

Let $\mathcal{A}$ be a finite-dimensional algebra over a finite field $\mathbf{F}_q$ and let $G=\mathcal{A}^\times$ be the multiplicative group of $\mathcal{A}$. In this paper, we construct explicitly a generic Galois $G$-extension $S/R$, where $R$ is a localized polynomial ring over $\mathbf{F}_q$, and an explicit generic polynomial for $G$ in $\dim_{\mathbf{F}_q}(\mathcal{A})$ parameters.

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BibTeX RIS

Jorge Morales, Anthony Sanchez. 2014-05-30. Generic extensions and generic Polynomials for multiplicative groups. https://arxiv.org/abs/1405.7807

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