Abstract.
The minimal homogeneous basis is defined. It is shown that every minimal homogeneous basis of an ideal has the same number of elements. An algorithm for finding a minimal homogeneous basis is developed. The main idea is to modify the classical Buchberger’s algorithm for finding a Gröbner basis so that a minimal homogeneous basis can be obtained as a subset of a Gröbner basis.
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References
Ferro, G.C., Robbiano, L.: On superG-bases. J. Pure Appl. Algebra 68, 279–292 (1990)
Cox, D., Little, J., O’Shea, D.: Ideals, Varieties and Algorithms. Springer-Verlag, 1992
Cox, D., Little, J., O’Shea, D.: Using Algebraic Geometry. Springer-Verlag, 1999
Luo, T., Yilmaz, E.: On the Lifting Problem for Homogeneous Ideals. J. Pure Appl. Algebra 162, 327–335 (2001)
Roitman, M.: On the lifting Problem for Homogeneous Ideals in Polynomial Rings. J. Pure Appl. Algebra 51, 205–215 (1988)
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Yılmaz, E., Kılıçarslan, S. Minimal Homogeneous Bases for Polynomial Ideals. AAECC 15, 267–278 (2004). https://doi.org/10.1007/s00200-004-0159-3
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DOI: https://doi.org/10.1007/s00200-004-0159-3