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arXiv · 1302.1852

Torsion in tensor products, and tensor powers, of modules

Olgur Celikbas·Srikanth B. Iyengar·Greg Piepmeyer·Roger Wiegand
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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.

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Olgur Celikbas, Srikanth B. Iyengar, Greg Piepmeyer, Roger Wiegand. 2013-02-07. Torsion in tensor products, and tensor powers, of modules. https://arxiv.org/abs/1302.1852

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