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.
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