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m-full ideals II

Published online by Cambridge University Press:  24 October 2008

Junzo Watanabe
Affiliation:
Department of Mathematics, Hokkaido Tokai University, 5111 Minamisawa, Minamiku Sapporo 005, Japan

Extract

In his paper 10 the author investigated the structure of m-full ideals by analysing their syzygies and, as one special case, showed how the Betti numbers of Borel stable ideals over polynomial rings can be computed. The same result, among other things, was also obtained by Eliahou and Kervaire1 by a different method.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

REFERENCES

1Eliahou, S. and Kervaire, M.. Minimal free resolutions of some monomial ideals. J. Algebra 129 (1990), 125.CrossRefGoogle Scholar
2Elias, J., Robbiano, L. and Valla, G.. Number of generators of ideals. Nagoya Math. J., to appear.Google Scholar
3Green, M.. Restrictions of linear series to hyperplanes, and some results of Macaulay and Gotzmann. In Algebraic Curves and Protective Geometry (eds. Ballico, E. and Ciliberto, C.), Lecture Notes in Math. vol. 1389 (Springer-Verlag, 1989), pp. 7686.CrossRefGoogle Scholar
4Greene, C. and Kleitman, D. J.. Proof techniques in the theory of finite sets. In Studies in Combinatorics (ed. Rota, G.-C.) (Mathematical Association of America, 1978), pp. 2279.Google Scholar
5Kruskal, J.. The number of simplices in a complex. In Mathematical Optimization Techniques (University of California Press, 1963), pp. 251278.CrossRefGoogle Scholar
6Macaulay, F. S.. Some properties of enumeration in the theory of modular systems. Proc. London Math. Soc. 26 (1927), 531555.CrossRefGoogle Scholar
7Sally, J.. Numbers of Generators of Ideals in Local Rings. Lecture Notes in Pure and Appl. Math. vol. 35 (Marcel Dekker, 1978).Google Scholar
8Stanley, R.. Combinatorics and Commutative Algebra. Progress in Math. no. 41 (Birkhuser, 1983).CrossRefGoogle Scholar
9Stanley, R.. Hilbert function of graded algebras. Adv. in Math. 28 (1978), 5783.CrossRefGoogle Scholar
10Watanabe, J.. The syzygies of m-full ideals. Math. Proc. Cambridge Philos. Soc. 109 (1991), 713.CrossRefGoogle Scholar
11Watanabe, J.. m-Full ideals. Nagoya Math. J. 106 (1987), 101111.CrossRefGoogle Scholar