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Non-commutative Gröbner bases for commutative algebras

Author(s): David Eisenbud; Irena Peeva; Bernd Sturmfels
Journal: Proc. Amer. Math. Soc. 126 (1998), 687-691.
MSC (1991): Primary 13P10, 16S15
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Abstract: An ideal $I$ in the free associative algebra $k\langle X_{1},\dots ,X_{n}\rangle $ over a field $k$ is shown to have a finite Gröbner basis if the algebra defined by $I$ is commutative; in characteristic 0 and generic coordinates the Gröbner basis may even be constructed by lifting a commutative Gröbner basis and adding commutators.

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Additional Information:

David Eisenbud
Affiliation: MSRI, 1000 Centennial Dr., Berkeley, California 94720
Email: de@msri.org

Irena Peeva
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: irena@math.mit.edu

Bernd Sturmfels
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Email: bernd@math.berkeley.edu

DOI: 10.1090/S0002-9939-98-04229-4
PII: S 0002-9939(98)04229-4
Received by editor(s): September 6, 1996
Additional Notes: The first and third authors are grateful to the NSF and the second and third authors are grateful to the David and Lucille Packard Foundation for partial support in preparing this paper.
Communicated by: Wolmer V. Vasconcelos
Copyright of article: Copyright 1998, American Mathematical Society

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