Torsion and tensor products over domains and specializations to semigroup rings

Let R be a commutative Noetherian domain, and let M and N be finitely generated R  -modules. We give new criteria for determining when the tensor product of two modules has torsion. We also give constructive formulas for the torsion submodule of M⊗RNM⊗RN. In certain cases we determine bounds on the length and minimal number of generators of the torsion submodule. Lastly, we focus on the case where R is a numerical semigroup ring with the goal of making progress on the Huneke–Wiegand Conjecture.