Iterative Derivations on Central Simple Algebras
Abstract
We prove that an iterative derivation δF on a field F can be extended to an iterative derivation δA on a central simple F-algebra A if the characteristic of F does not divide the exponent of A in the Brauer group of F. For a central simple F-algebra with an iterative derivation, we show the existence of a unique (up to isomorphism) Picard-Vessiot splitting field and from the nature its Galois group, we also describe the structure of the central simple algebra in terms of its δA-right ideals.
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