Homomorphisms of modules associated with polynomial matrices with infinite elementary divisors

TL;DR

This paper characterizes module homomorphisms associated with polynomial matrices that have polynomial parts of their inverses, revealing structural insights at infinity for modules over rational functions.

Contribution

It introduces a characterization of homomorphisms of modules linked to polynomial matrices with infinite elementary divisors, focusing on their structure at infinity.

Findings

Homomorphisms are characterized in relation to polynomial matrices with polynomial inverse parts.

The module structure over proper rational functions is analyzed at infinity.

Results connect the algebraic structure of modules to the properties of polynomial matrices.

Abstract

If the inverse of a nonsingular polynomial matrix $L$ has a polynomial part then one can associate with $L$ a module over the ring of proper rational functions, which is related to the structure of $L$ at infinity. In this paper we characterize homomorphisms of such modules.