Algebraic Families of Subfields in Division Rings

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Daneshvar, Asghar | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 43429 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Hezavehi, Mohammad
Abstract:
If L is a finite-dimensional Lie algebra over the field F then the universal enveloping algebra U(L) can be embedded in a division ring D. In particular, if L is a solvable p-algebra, there is a decomposition D=KR where K and R are maximal subfields of D, K is Galois extension of the center Z of D and R is a purely inseparable extension of Z with R^p⊆Z. The present thesis is concerned with the compared structures of maximal subfields in a division D and in the division ring of rational functions D(X). We prove that maximal subfields of D(X) “generically” specialize to maximal subfields of D, and properties such as being Galois or purely inseparable over the centre also carry over generically.
Keywords:
Maximal Subfield ; BRAUER GROUP ; Division Rings ; Enveloping Algebra

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