  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.
