English

Torsion in tensor products, and tensor powers, of modules

Commutative Algebra 2014-12-23 v2

Abstract

For finitely generated modules M and N over a complete intersection R, the vanishing of Tor_i^R(M,N) for all i> 0 gives a tight relationship among depth properties of M, N and their tensor product. Here we concentrate on the converse and show, under mild conditions, that the tensor product of M and N being torsion-free (or satisfying higher Serre conditions) forces vanishing of Tor. Special attention is paid to the case of tensor powers of a single module.

Keywords

Cite

@article{arxiv.1302.1852,
  title  = {Torsion in tensor products, and tensor powers, of modules},
  author = {Olgur Celikbas and Srikanth B. Iyengar and Greg Piepmeyer and Roger Wiegand},
  journal= {arXiv preprint arXiv:1302.1852},
  year   = {2014}
}

Comments

The results in this paper have been absorbed into arXiv:1412.6454 and arXiv:1412.6456