Powers of ideals: Primary decompositions, Artin-Rees lemma and regularity

Mathematische Annalen

Volumn 307, Issue 2, 1997, Pages 299-313

  Swanson, Irena ^a  

^a NEW MEXICO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031538222     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002080050035     Document Type: Article

References (15)

1. D. Bayer, M. Stillman: A criterion for detecting m-regularity. Invent. Math. 87 (1987), 1-11.
2. K. A. Chandler: Regularity of the powers of an ideal 1. Preprint.
3. D. Eisenbud, C. Huneke, W. Vasconcelos: Direct methods for primary decomposition. Invent. math. 110 (1992), 207-235.
4. A. V. Geramita, A. Gimigliano, Y. Pitteloud: Graded Belli numbers of some embedded rational n-folds. Math. Ann. 301 (1995), 363-380.
5. W. Heinzer, I. Swanson: Ideals contracted from 1-dimensional overrings with an application to the primary decomposition of ideals. Preprint.
6. J. Herzog: A homological approach to symbolic powers. In: Commutative Algebra, Proc. of a Workshop held in Salvador, Brazil, 1988. Lecture Notes in Mathematics 1430, 32-46. Springer-Verlag, Berlin, 1990.
7. M. Hochster, C. Huneke: F-regularity, test elements, and smooth base change. Trans. Amer. Math. Soc. 346 (1994), 1-62.
8. C. Huneke: Uniform bounds in Noetherian rings Invent. Math. 107 (1992), 203-223.
9. D. Katz, S. McAdam: Two asymptotic functions, Comm. in Alg. 17 (1989), 1069-1091.
10. e(M) and its connections to tight closure. Preprint.
11. D. G. Northcott, D. Rees: Reductions of ideals in local rings. Proc. Cambridge Phil. Soc. 50 (1954), 145-158.
12. n, n large. Michigan Math. J. 23 (1976), 337-352.
13. Karen E. Smith, I. Swanson: Linear bounds on growth of associated primes for monomial ideals: Preprint.
14. B. Sturmfels, N. V. Trung, W. Vogel: Bounds on degrees of projective schemes, Math. Annalen 302 (1995), 417-432.
15. I. Swanson: Primary decompositions of powers of ideals. "Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra: Proceedings of a summer research conference on commutative algebra held July 4-10, 1992" (W. Heinzer, C. Huneke, J. D. Sally, ed.). Contemporary Mathematics, Volume 159. Amer. Math. Soc., Providence, 1994, pp. 367-371.