Complexity of tensor products of modules and a theorem of huneke-wiegand

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14 Scopus citations

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 ToriR (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.

Original languageEnglish (US)
Pages (from-to)53-60
Number of pages8
JournalProceedings of the American Mathematical Society
Volume126
Issue number1
StatePublished - Dec 1 1998
Externally publishedYes

Keywords

  • Complete intersection
  • Complexity
  • Hypersurface
  • Rigidity
  • Tensor product

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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