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Torsion in tensor powers of modules

Part of: Theory of modules and ideals Commutative algebra: Homological methods

Published online by Cambridge University Press:  11 January 2016

Olgur Celikbas ,
Srikanth B. Iyengar ,
Greg Piepmeyer  and
Roger Wiegand
Olgur Celikbas
Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211, USA
Srikanth B. Iyengar
Affiliation:
Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588-0130, USA
Greg Piepmeyer
Affiliation:
Columbia Basin College Pasco, Washington 99301, USA
Roger Wiegand
Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211, USA
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Abstract

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Tensor products usually have nonzero torsion. This is a central theme of Auslander's 1961 paper; the theme continues in the work of Huneke and Wiegand in the 1990s. The main focus in this article is on tensor powers of a finitely generated module over a local ring. Also, we study torsion-free modules N with the property that M ⊗R N has nonzero torsion unless M is very special. An important example of such a module N is the Frobenius power peR over a complete intersection domain R of characteristic p > 0.

MSC classification

Secondary: 13C12: Torsion modules and ideals 13D07: Homological functors on modules (Tor, Ext, etc.)
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 219 , September 2015 , pp. 113 - 125
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2015

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