Galois groups over rational function fields over skew fields

2020/02/24 by Gil Alon, Alon, Gil, François Legrand +3
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2002.10300

openalex publication_date 2020/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H be a skew field of finite dimension over its center k. We solve the Inverse Galois Problem over the field of fractions H(X) of the ring of polynomial functions over H in the variable X, if k contains an ample field.

Citations

• Theory of Non-Commutative Polynomials
• A Quaternionic Nullstellensatz

Related

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• Théorie inverse de Galois sur les corps des fractions rationnelles tordus
• Regular version of the inverse Galois problem for skew fields
• Problèmes de plongement finis sur les corps non commutatifs
• Inverse Galois Problem and Significant Methods