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Links of prime ideals

Published online by Cambridge University Press:  24 October 2008

Alberto Corso ,
Claudia Polini  and
Wolmer V. Vasconcelos
Alberto Corso
Affiliation:
Department of Mathematics, Rutgers University. New Brunswick, New Jersey 08903
Claudia Polini
Affiliation:
Department of Mathematics, Rutgers University. New Brunswick, New Jersey 08903
Wolmer V. Vasconcelos
Affiliation:
Department of Mathematics, Rutgers University. New Brunswick, New Jersey 08903
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Extract

Roughly speaking, a link of an ideal of a Noetherian ring R is an ideal of the form I = (z): , where z = z1, …, zg is a regular sequence and g is the codimension of . This is a very common operation in commutative algebra, particularly in duality theory, and plays an important role in current methods to effect primary decomposition of polynomial ideals (see [2]).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 115 , Issue 3 , May 1994 , pp. 431 - 436
Copyright
Copyright © Cambridge Philosophical Society 1994

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References

REFERENCES

[1]Eagon, J. and Northcott, D. G.. Ideals defined by matrices and a certain complex associated with them. Proc. Royal Soc. 269 (1962), 188–204.Google Scholar
[2]Eisenbud, D., Huneke, C. and Vasconcelos, W. V.. Direct methods for primary decomposition. Invent. Math. 110 (1992), 207–235.CrossRefGoogle Scholar
[3]Herzog, J. and Kunz, E.. Der kanonische Modul eines Cohen–Macaulay Rings. Lecture Notes in Mathematics 238 (Springer-Verlag, 1971).CrossRefGoogle Scholar
[4]Herzog, J., Simis, A. and Vasconcelos, W. V.. Koszul homology and blowing-up rings. In Commutative Algebra, Proceedings: Trento 1981 (Greco, S. and Valla, G., Eds.), Lecture Notes in Pure and Applied Math. 84 (Marcel Dekker, 1983), 79–169.Google Scholar
[5]Huckaba, S. and Huneke, C.. Powers of ideals having small analytic deviation. Amer. J. Math. 114 (1992), 367–403.CrossRefGoogle Scholar
[6]Ikeda, S. and Trung, N. V.. When is the Rees algebra Cohen–Macaulay?. Comm. Algebra 17 (1989), 2893–2922.Google Scholar
[7]Matsumura, H.. Commutative Ring Theory (Cambridge University Press, 1986).Google Scholar
[8]Northcott, D. G.. A homological investigation of a certain residual ideal. Math. Ann. 150 (1963), 99–110.CrossRefGoogle Scholar
[9]Northcott, D. G. and Rees, D.. Reductions of ideals in local rings. Proc. Camb. Phil. Soc. 50 (1954), 145–158.CrossRefGoogle Scholar
[10]Peskine, C. and Szpiro, L.. Liaison des variétés algébriques. Invent. Math. 26 (1974), 271–302.CrossRefGoogle Scholar
[11]Simis, A. and Vasconcelos, W. V.. The syzygies of the conormal module. Amer. J. Math. 103 (1981), 203–224.CrossRefGoogle Scholar