Torsion and Tensor Products Over Domains and Specializations to Semigroup Rings

2012/11/13 by Leamer, Micah Josiah
#13A99 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1211.2896

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.

Related

• Torsion in tensor powers of modules
• Endomorphism algebras over commutative rings and torsion in self tensor products
• Length complexity of tensor products
• Torsion in tensor products over one-dimensional domains
• Serre's condition for tensor products and n-Tor-rigidity of modules