English

Iterative Derivations on Central Simple Algebras

Rings and Algebras 2026-01-23 v1

Abstract

We prove that an iterative derivation δF\delta_F on a field FF can be extended to an iterative derivation δA\delta_A on a central simple FF-algebra AA if the characteristic of FF does not divide the exponent of AA in the Brauer group of F.F. For a central simple FF-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\delta_A-right ideals.

Keywords

Cite

@article{arxiv.2601.15648,
  title  = {Iterative Derivations on Central Simple Algebras},
  author = {Manujith K. Michel and Varadharaj R. Srinivasan},
  journal= {arXiv preprint arXiv:2601.15648},
  year   = {2026}
}
R2 v1 2026-07-01T09:15:14.597Z