Two Remarks on Independent Sets
Hans-Gert Gräbe
DOI: 10.1023/A:1022459607909
Abstract
In the first part we generalize the notion of strongly independent sets, introduced in [10] for polynomial ideals, to submodules of free modules and explain their computational relevance. We discuss also two algorithms to compute strongly independent sets that rest on the primary decomposition of squarefree monomial ideals.
Usually the initial ideal in( I) of a polynomial ideal I is worse than I. In [9] the authors observed that nevertheless in( I) is not as bad as one should expect, showing that in( I) is connected in codimension one if I is prime.
Pages: 137–145
Keywords: independent set; initial ideal; unmixedness; connectedness in codimension
Full Text: PDF
References
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8. H.-G. Grabe, CALl-A REDUCE Package for Commutative Algebra, Version 1.0, 1992 (available
2. D. Bayer and M. Stillman, "Computation of Hilbert functions," J. Symb. Comp. 14 (1992), 31-50.
3. A.M. Bigatti, P. Conti, L. Robbiano, and C. Traverso, "A divide and conquer algorithm for Hilbert-Poincare series, multiplicity and dimension of monomial ideals," to appear.
4. G. Carra Ferro, "Some properties of the lattice points and their application to differential algebra," Comm. Alg. 15 (1987), 2625-2632.
5. W. Fulton and J. Hansen, "A connectedness theorem for projective varieties, with applications to intersections and singularities of mappings," Ann. Math. 110 (1981), 26-92.
6. H.-G. Grabe, "Uber den Stanley-Reisner-Ring von Quasimannigfaltigkeiten," Math. Nachr. 117 (1984), 161-174.
7. H.-G. Grabe, "Moduln iiber Streckungsringen," Results in Math.15 (1989), 202-220.
8. H.-G. Grabe, CALl-A REDUCE Package for Commutative Algebra, Version 1.0, 1992 (available
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