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 | References | Similar Articles | Additional Information

Abstract: An ideal in the free associative algebra over a field is shown to have a finite Gröbner basis if the algebra defined by 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