2010/11/02 by Jean-Marie Bois, J. M. Bois, Bois, J. M. +3
Mathematics · #16K20 (Primary) 14A25 #17B35 #17B50 (Secondary) #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.AG #math.RA #msc:14A25 #msc:16K20 #msc:17B35 #msc:17B50
paper · pdf · doi:10.48550/arxiv.1011.0584
9 pages, revised according to referee comments, new title
openalex publication_date 2010/11/02 · arxiv created 2011/03/23 · arxiv updated 2011/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe relations between maximal subfields in a division ring and in its rational extensions. More precisely, we prove that properties such as being Galois or purely inseparable over the centre generically carry over from one to another. We provide an application to enveloping skewfields in positive characteristics. Namely, there always exist two maximal subfields of the enveloping skewfield of a solvable Lie algebra, such that one is Galois and the second purely inseparable of exponent 1 over the centre. This extends results of Schue in the restricted case. Along the way we provide a description of the enveloping algebra of the p-envelope of a Lie algebra as a polynomial extension of the smaller enveloping algebra.