Algebraic families of subfields in division rings

JOURNAL OF ALGEBRA

卷:339

Article

Bois, Jean-Marie¹  Vernik, Gil¹ 

[1] Univ Kiel, Math Seminar, D-24098 Kiel, Germany

关键词: Division ring;    Maximal subfield;    Brauer group;    Enveloping algebra;   

DOI  :  10.1016/j.jalgebra.2011.03.035

来源: Elsevier

【 摘 要 】

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 (Schue, 1990 [5]). 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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free