Regular singular differential modules over differential rings

TL;DR

This paper extends the Fuchs decomposition theorem to regular singular differential modules over broad differential rings, linking regularity with differential Galois theory and automorphism-based vector spaces.

Contribution

It introduces a new definition of regularity and proves a generalized Fuchs decomposition theorem for differential modules over diverse differential rings.

Findings

Established Fuchs decomposition for regular singular modules over new classes of rings

Connected regularity with differential Galois theory and automorphisms

Provided a generalized framework for analyzing differential modules

Abstract

We obtain Fuchs decomposition theorem for regular singular differential modules over a large class of differential rings. We provide a definition of regularity inspired by differential Galois theory and we deduce the classical equivalence with vector spaces endowed with an automorphism.