Iterative Derivations on Central Simple Algebras
Rings and Algebras
2026-01-23 v1
Abstract
We prove that an iterative derivation on a field can be extended to an iterative derivation on a central simple algebra if the characteristic of does not divide the exponent of in the Brauer group of For a central simple 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 right ideals.
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}
}