Ideal and subalgebra coefficients
Authors:
Lorenzo Robbiano and Moss Sweedler
Journal:
Proc. Amer. Math. Soc. 126 (1998), 22132219
MSC (1991):
Primary 13P10; Secondary 12Y05
MathSciNet review:
1443407
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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:
http://dx.doi.org/10.1090/S0002993998043068
PII:
S 00029939(98)043068
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 DAAL0391C0027, and by the NSA
Communicated by:
Wolmer V. Vasconcelos
Article copyright:
© Copyright 1998
American Mathematical Society
