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

DOI:
https://doi.org/10.1090/S0002-9939-98-04306-8

MathSciNet review:
1443407

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Abstract | References | Similar Articles | Additional Information

Abstract: For an ideal or -subalgebra of , consider subfields , where is generated - as ideal or -subalgebra - by polynomials in . It is a standard result for ideals that there is a smallest such . We give an algorithm to find it. We also prove that there is a smallest such for -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:
https://doi.org/10.1090/S0002-9939-98-04306-8

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