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We show that over a complete intersection R the complexity of the tensor product $M\\otimes\\sb{R}N$ of two finitely generated modules is the sum of the complexities of each if $Tor\\sbsp{i}{R}(M,\\ N)=0$ for $i\\ge1.$ One of the applications is simplification of the proofs of central results over hypersurface rings in a paper of C. Huneke and R. Wiegand on the tensor product of modules and the rigidity of Tor (HW1).","Made available in DSpace on 2015-09-28T15:20:20Z (GMT). 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