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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Non-commutative Gröbner bases
for commutative algebras


Authors: David Eisenbud, Irena Peeva and Bernd Sturmfels
Journal: Proc. Amer. Math. Soc. 126 (1998), 687-691
MSC (1991): Primary 13P10, 16S15
DOI: https://doi.org/10.1090/S0002-9939-98-04229-4
MathSciNet review: 1443825
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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: https://doi.org/10.1090/S0002-9939-98-04229-4
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
Article copyright: © Copyright 1998 American Mathematical Society