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Differential Operators on Finite Purely Inseparable Extensions

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posted on 24.10.2013, 00:00 authored by Matthew A. Wechter
We study the the differential operators of a finite modular field extension. Using the Jacobson-Bourbaki Theorem, we establish criteria for when a subalgebra of the differential operators on an extension corresponds to an intermediate modular extension. Furthermore, we can determine when an extension is modular using a sequence of modules of differentials. Finally, this thesis will clarify and expand on Gerstenhaber's theory of higher derivations and their correspondences with modular extensions, and we determine criteria for when a subspace of the symbol algebra corresponds to an intermediate extension in a simple example.

History

Advisor

Gillet, Henri

Department

Mathematics, Statistics, and Computer Science

Degree Grantor

University of Illinois at Chicago

Degree Level

Doctoral

Committee Member

Coskun, Izzet Popa, Mihnea Takloo-Bighash, Ramin Hoobler, Raymond

Submitted date

2013-08

Language

en

Issue date

24/10/2013

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