On subdirect factors of a projective module and applications to system theory

TL;DR

This paper generalizes a known result about projective modules over Noetherian domains, providing a system-theoretic interpretation and showing that certain subdirect product structures imply projectivity of torsion-free factors.

Contribution

It extends previous results to the noncommutative case and introduces a system-theoretic perspective on subdirect factors of projective modules.

Findings

Subdirect product structures imply projectivity of torsion-free factors.

Extension of results to noncommutative Noetherian domains.

System-theoretic interpretation of module decomposition.

Abstract

We extend a result of Napp Avelli, van der Put, and Rocha with a system-theoretic interpretation to the noncommutative case: Let P be a f.g. projective module over a two-sided Noetherian domain. If P admits a subdirect product structure of the form P = M x_T L over a factor module T of grade at least 2 then the torsion-free factor of M (resp. L) is projective.