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arXiv · 1412.6454

Torsion in tensor powers of modules

Olgur Celikbas·Srikanth B. Iyengar·Greg Piepmeyer·Roger Wiegand
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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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Olgur Celikbas, Srikanth B. Iyengar, Greg Piepmeyer, Roger Wiegand. 2014-12-19. Torsion in tensor powers of modules. https://arxiv.org/abs/1412.6454

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