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