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

Claudia Miller

doi:10.1090/s0002-9939-98-04017-9

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

Claudia Miller

Research output: Contribution to journal › Article › peer-review

19 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 Tor_i^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.

Original language	English (US)
Pages (from-to)	53-60
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	126
Issue number	1
DOIs	https://doi.org/10.1090/s0002-9939-98-04017-9
State	Published - 1998
Externally published	Yes

Keywords

Complete intersection
Complexity
Hypersurface
Rigidity
Tensor product

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/s0002-9939-98-04017-9

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AB - 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.

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KW - Rigidity

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

Abstract

Keywords

ASJC Scopus subject areas

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