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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Complexity of tensor products of modules
and a theorem of Huneke-Wiegand


Author: Claudia Miller
Journal: Proc. Amer. Math. Soc. 126 (1998), 53-60
MSC (1991): Primary 13C14, 13C40, 13D05, 13D40, 13H10
MathSciNet review: 1415354
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Abstract | References | Similar Articles | Additional Information

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.


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Additional 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

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04017-9
PII: S 0002-9939(98)04017-9
Keywords: Complexity, complete intersection, hypersurface, rigidity, tensor product
Received by editor(s): March 25, 1996
Received by editor(s) in revised form: July 5, 1996
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1998 American Mathematical Society