On modules over Laurent polynomial rings

TL;DR

This paper characterizes finitely generated modules over Laurent polynomial rings using sub-lattices, linking algebraic properties to applications in knot theory.

Contribution

It provides a novel lattice-based description of modules over Laurent polynomial rings, connecting algebraic invariants to topological applications.

Findings

Modules without Z-torsion are determined by sub-lattices of L^d.

Indices of sub-lattices relate to leading and trailing coefficients of module order.

Application to knot theory invariants.

Abstract

A finitely generated module over the ring L=Z[t, t^{-1}] of integer Laurent polynomials that has no Z-torsion is determined by a pair of sub-lattices of L^d. Their indices are the absolute values of the leading and trailing coefficients of the order of the module. This description has applications in knot theory.