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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Ideal and subalgebra coefficients


Authors: Lorenzo Robbiano and Moss Sweedler
Journal: Proc. Amer. Math. Soc. 126 (1998), 2213-2219
MSC (1991): Primary 13P10; Secondary 12Y05
MathSciNet review: 1443407
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Abstract: For an ideal or $K$-subalgebra $E$ of $K[X_1,\dots,X_n]$, consider subfields $k\subset K$, where $E$ is generated - as ideal or $K$-subalgebra - by polynomials in $k[X_1,\dots,X_n]$. It is a standard result for ideals that there is a smallest such $k$. We give an algorithm to find it. We also prove that there is a smallest such $k$ for $K$-subalgebras. The ideal results use reduced Gröbner bases. For the subalgebra results we develop and then use subduced SAGBI (bases), the analog to reduced Gröbner bases.


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Additional Information

Lorenzo Robbiano
Affiliation: Department of Mathematics, University of Genoa, Italy
Email: robbiano@dima.unige.it

Moss Sweedler
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
Email: moss_sweedler@cornell.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04306-8
PII: S 0002-9939(98)04306-8
Keywords: Ideal, subalgebra, field of definition, reduced Gr\"obner basis, subduced SAGBI (basis)
Received by editor(s): August 29, 1996
Received by editor(s) in revised form: January 16, 1997
Additional Notes: The first author was partially supported by the Consiglio Nazionale delle Ricerche (CNR)
The second author was partially supported by the United States Army Research Office through the Army Center of Excellence for Symbolic Methods in Algorithmic Mathematics (ACSyAM), Mathematical Sciences Institute of Cornell University, Contract DAAL03-91-C-0027, and by the NSA
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1998 American Mathematical Society