Jordan-Chevalley decompositions over imperfect fields

TL;DR

This paper classifies Jordan-Chevalley decompositions of endomorphisms over imperfect fields, extending understanding beyond perfect fields by analyzing additive decompositions into commuting semisimple and nilpotent parts.

Contribution

It provides a classification of Jordan-Chevalley decompositions over imperfect fields, a case less understood in linear algebra.

Findings

Classifies Jordan-Chevalley decompositions over imperfect fields.

Describes conditions for additive decompositions into semisimple and nilpotent endomorphisms.

Extends existing theory from perfect to imperfect fields.

Abstract

We give a classification of Jordan-Chevalley decompositions of an endomorphism of a finite-dimensional vector space over a not necessarily perfect field, i.e. additive decompositions into commuting semisimple and nilpotent endomorphisms.