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Complexity of Tensor Products of Modules and a Theorem of Huneke-Wiegand

Claudia Miller
Proceedings of the American Mathematical Society
Vol. 126, No. 1 (Jan., 1998), pp. 53-60
Stable URL: http://www.jstor.org/stable/118825
Page Count: 8
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Complexity of Tensor Products of Modules and a Theorem of Huneke-Wiegand
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Abstract

This paper concerns the notion of complexity, a measure of the growth of the Betti numbers of a module. We show that over a complete intersection R the complexity of the tensor product M ⊗ R N of two finitely generated modules is the sum of the complexities of each if Tori R(M, N) = 0 for i ≥ 1. One of the applications is simplification of the proofs of central results in a paper of C. Huneke and R. Wiegand on the tensor product of modules and the rigidity of Tor.

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