Torsion and Tensor Products Over Domains and Specializations to Semigroup Rings

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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.