Torsion in tensor products over one-dimensional domains

Neil Steinburg; RogerWiegand

Torsion in tensor products over one-dimensional domains

Commutative Algebra 2019-02-20 v1

Authors: Neil Steinburg , RogerWiegand

Abstract

Over a one-dimensional Gorenstein local domain $R$ , let $E$ be the endomorphism ring of the maximal of $R$ , viewed as a subring of the integral closure $\overline R$ . If there exist finitely generated $R$ -modules $M$ and $N$ , neither of them free, whose tensor product is torsion-free, we show that $E$ must be local with the same residue field as $R$ .

Keywords

one-dimensional domain gorenstein local ring tensor product torsion-free module endomorphism ring

Cite

@article{arxiv.1902.07157,
  title  = {Torsion in tensor products over one-dimensional domains},
  author = {Neil Steinburg and RogerWiegand},
  journal= {arXiv preprint arXiv:1902.07157},
  year   = {2019}
}

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