Ideal and subalgebra coefficients
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- by Lorenzo Robbiano and Moss Sweedler PDF
- Proc. Amer. Math. Soc. 126 (1998), 2213-2219 Request permission
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.References
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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
- 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
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2213-2219
- MSC (1991): Primary 13P10; Secondary 12Y05
- DOI: https://doi.org/10.1090/S0002-9939-98-04306-8
- MathSciNet review: 1443407