English

Torsion in tensor powers of modules

Commutative Algebra 2014-12-22 v1

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.

Keywords

Cite

@article{arxiv.1412.6454,
  title  = {Torsion in tensor powers of modules},
  author = {Olgur Celikbas and Srikanth B. Iyengar and Greg Piepmeyer and Roger Wiegand},
  journal= {arXiv preprint arXiv:1412.6454},
  year   = {2014}
}

Comments

10 pages; to appear in the Nagoya Math. Journal. arXiv admin note: substantial text overlap with arXiv:1302.1852

R2 v1 2026-06-22T07:38:30.325Z