Differential Operators on Finite Purely Inseparable Extensions
Wechter, Matthew A.
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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.
purely inseparable extension