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On coefficient ideals

Published online by Cambridge University Press:  11 June 2018

R. CALLEJAS-BEDREGAL ,
V. H. JORGE PÉREZ  and
M. DUARTE FERRARI
R. CALLEJAS-BEDREGAL
Affiliation:
Departamento de Matemática, CCEN - Centro de Ciências Exatas e da Natureza, UFPB - Universidade Federal da Paraíba e-mail: roberto@mat.ufpb.br
V. H. JORGE PÉREZ
Affiliation:
Departamento de Matemática, ICMC - Instituto de Ciências da Computação e Matemática, USP - Universidade de São Paulo e-mail: vhjperez@icmc.usp.br
M. DUARTE FERRARI
Affiliation:
Departamento de Matemática, CCE - Centro de Ciências Exatas, UEM - Universidade Estadual de Maringá e-mail: mdsilva@uem.br
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Abstract

Let (R, 𝔪) be a Noetherian local ring and I an arbitrary ideal of R with analytic spread s. In [3] the authors proved the existence of a chain of ideals I ⊆ I[s] ⊆ ⋅⋅⋅ ⊆ I[1] such that deg(PI[k]/I) < s − k. In this article we obtain a structure theorem for this ideals which is similar to that of K. Shah in [10] for 𝔪-primary ideals.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 167 , Issue 2 , September 2019 , pp. 285 - 294
Copyright
Copyright © Cambridge Philosophical Society 2018 

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References

REFERENCES

[1] Amao, J. O. On a certain Hilbert polynomial. J. London Math. Soc. (2) 14, 1 (1976), 13–20.Google Scholar
[2] Callejas–Bedregal, R., Pérez, V. H. Jorge and Silva, M. D.. On coefficient modules and Ratliff–Rush closure. Preprint.Google Scholar
[3] Herzog, J., Puthenpurakal, T. and Verma, J. K. Hilbert polynomials and powers of ideals. Math. Proc. Camb. Phil. Soc. 145 (2008), 623–642.Google Scholar
[4] Huneke, C. and Swanson, I. Integral closure of ideals, rings and modules. London Math. Soc. Lecture Note Series (Cambridge University Press, 2006).Google Scholar
[5] McAdam, S. Asymptotic prime divisors. Lecture Notes in Math. 1023 (Springer-Verlag, Berlin, 1983).Google Scholar
[6] Ratliff, L. J. and Rush, D. Two notes on reductions of ideals. Indiana University Math J. 27 (1978), 929–934.Google Scholar
[7] Rees, D. $\Mathcal{A}$-transforms of local rings and a theorem on multiplicities of ideals. Cambridge Philos. Soc. 57 (1961), 8–17.Google Scholar
[8] Rees, D. Amao's theorem and reduction criteria. J. London Math. Soc. (2) 32 (1985), no. 3, 404–410.Google Scholar
[9] Rees, D. Lectures on the asymptotic theory of ideals. London Math. Soc. Lecture Note Series, 113 (Cambridge University Press, Cambridge, 1988).Google Scholar
[10] Shah, K. K. Coefficient ideals Trans. Math. Soc. 327 (1991), 373–384.Google Scholar
[11] Samuel, P. and Zariski, O. Commutative Algebra. Vol. II (Springer-Verlag, Berlin, 1975).Google Scholar