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Rigid Ideals in Gorenstein Rings of Dimension One

  • Craig HunekeEmail author
  • Srikanth B. Iyengar
  • Roger Wiegand
Article
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Abstract

Motivated by a conjecture of Huneke and Wiegand concerning torsion in tensor products of modules over local rings, we investigate the existence of ideals I in a one-dimensional Gorenstein local ring R satisfying \(\text {Ext}^{1}_{R}(I,I)= 0\).

Keywords

Complete intersection ring Gorenstein ring Rigid module Tensor product Torsion 

Mathematics Subject Classification (2010)

13D07 13C14 13C99 

Notes

Acknowledgements

We thank Adam Boocher, Olgur Celikbas, and Graham Leuschke for helpful comments during the preparation of this work. We also are grateful to various referees for their detailed comments on an earlier version of this paper.

Funding Information

This article is based on work supported by the National Science Foundation under Grant No. 0932078000, while the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Fall semester of 2012. The first author was partially supported by NSF grant DMS-1460638; the second author partly supported by NSF grant DMS-1700985; the third author partly supported by Simons Collaboration Grants 209213 and 426885.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Craig Huneke
    • 1
    Email author
  • Srikanth B. Iyengar
    • 2
  • Roger Wiegand
    • 3
  1. 1.Department of MathematicsUniversity of VirginiaCharlottsvilleUSA
  2. 2.Department of MathematicsUniversity of UtahSalt Lake CityUSA
  3. 3.Department of MathematicsUniversity of NebraskaLincolnUSA

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