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arXiv · 2601.15648

Iterative Derivations on Central Simple Algebras

Manujith K. Michel·Varadharaj R. Srinivasan
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Abstract

We prove that an iterative derivation $\delta_F$ on a field $F$ can be extended to an iterative derivation $\delta_A$ 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 $\delta_A-$right ideals.

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Manujith K. Michel, Varadharaj R. Srinivasan. 2026-01-22. Iterative Derivations on Central Simple Algebras. https://arxiv.org/abs/2601.15648

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