Some remarks on non-commutative principal ideal rings

TL;DR

This paper explores algebraic properties of matrix differential operator rings over differential fields within non-commutative principal ideal rings, with applications to non-local Poisson structures.

Contribution

It extends algebraic results to non-commutative principal ideal rings and applies them to the theory of non-local Poisson structures.

Findings

Proved algebraic properties of matrix differential operator rings.

Established connections to non-local Poisson structures.

Abstract

We prove some algebraic results on the ring of matrix differential operators over a differential field in the generality of non-commutative principal ideal rings. These results are used in the theory of non-local Poisson structures.