Torsion in tensor powers of modules

2014/12/19 by Olgur Celikbas, Celikbas, Olgur, Srikanth B. Iyengar +5
Mathematics · #13C40 #13D07 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1412.6454

openalex publication_date 2014/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Tensor products usually have nonzero torsion. This is a central theme of Auslander's paper "Modules over unramified regular local rings"; the theme continues in the work of Huneke and Wiegand. The main focus in this note is on tensor powers of a finitely generated module over a local ring. Also, we study torsion-free modules N with the property that its tensor product with any module M has torsion, unless M is very special. Important examples of such modules N are the Frobenius power of a ring, viewed as a module over itself, that is a complete intersection domain of positive characteristic.

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• Torsion in tensor products, and tensor powers, of modules
• Torsion in tensor products over one-dimensional domains
• Torsion and Tensor Products Over Domains and Specializations to Semigroup Rings
• Endomorphism algebras over commutative rings and torsion in self tensor products
• Serre's condition for tensor products and n-Tor-rigidity of modules