Generic extensions and generic Polynomials for multiplicative groups
Jorge Morales, Anthony Sanchez

TL;DR
This paper constructs explicit generic Galois extensions and polynomials for multiplicative groups of finite-dimensional algebras over finite fields, advancing the understanding of their algebraic and Galois-theoretic properties.
Contribution
It provides explicit constructions of generic Galois extensions and polynomials for multiplicative groups of finite-dimensional algebras over finite fields.
Findings
Explicit generic Galois $G$-extension $S/R$ constructed
Explicit generic polynomial for $G$ with $ ext{dim}_{f F_q}( ext{A})$ parameters
Advances in understanding Galois theory of multiplicative groups
Abstract
Let be a finite-dimensional algebra over a finite field and let be the multiplicative group of . In this paper, we construct explicitly a generic Galois -extension , where is a localized polynomial ring over , and an explicit generic polynomial for in parameters.
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