Complexity of tensor products of modules and a theorem of Huneke-Wiegand
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- by Claudia Miller
- Proc. Amer. Math. Soc. 126 (1998), 53-60
- DOI: https://doi.org/10.1090/S0002-9939-98-04017-9
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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 $M\otimes _{R} N$ of two finitely generated modules is the sum of the complexities of each if $\operatorname {Tor}_{i}^{R}(M,N)=0$ for $i\geq 1$. 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.References
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Bibliographic Information
- Claudia Miller
- Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
- Address at time of publication: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
- Email: cmiller@math.uiuc.edu
- Received by editor(s): March 25, 1996
- Received by editor(s) in revised form: July 5, 1996
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 53-60
- MSC (1991): Primary 13C14, 13C40, 13D05, 13D40, 13H10
- DOI: https://doi.org/10.1090/S0002-9939-98-04017-9
- MathSciNet review: 1415354