Torsion and Tensor Products Over Domains and Specializations to Semigroup Rings

TL;DR

This paper develops new criteria and formulas for analyzing torsion in tensor products of modules over Noetherian domains, with a focus on numerical semigroup rings to address the Huneke-Wiegand Conjecture.

Contribution

It introduces novel criteria and constructive formulas for torsion in tensor products over domains, especially for numerical semigroup rings, advancing understanding of the Huneke-Wiegand Conjecture.

Findings

Provided new criteria for torsion in tensor products

Derived formulas for the torsion submodule in specific cases

Established bounds on module length and generators

Abstract

Let R be a commutative Noetherian domain, and let M and N be finitely generated R-modules. We give new criteria for determining when M tensor N has torsion. We also give constructive formulas for producing a module in the isomorphism class of the torsion submodule of M tensor N. In some cases we determine bounds on the length and minimal number of generators of this module. We focus on the case where R is a numerical semigroup ring with the goal of making progress on the Huneke-Wiegand Conjecture.