Non-commutative Gröbner bases for commutative algebras
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- by David Eisenbud, Irena Peeva and Bernd Sturmfels PDF
- Proc. Amer. Math. Soc. 126 (1998), 687-691 Request permission
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.References
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Additional Information
- David Eisenbud
- Affiliation: MSRI, 1000 Centennial Dr., Berkeley, California 94720
- MR Author ID: 62330
- ORCID: 0000-0002-5418-5579
- Email: de@msri.org
- Irena Peeva
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- MR Author ID: 263618
- Email: irena@math.mit.edu
- Bernd Sturmfels
- Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
- MR Author ID: 238151
- Email: bernd@math.berkeley.edu
- 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 1998 American Mathematical Society
- 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