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On the number of generators of powers of an ideal

Author: Judith D. Sally
Journal: Proc. Amer. Math. Soc. 53 (1975), 24-26
MSC: Primary 13A15
MathSciNet review: 0392969
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Abstract: Let $ I$ be an ideal of a quasi-local ring. In this note we consider the question of how small--in terms of numbers of generators--the powers of the ideal $ I$ can be.

References [Enhancements On Off] (What's this?)

  • [1] R. Gilmer, On factorization into prime ideals, Comment. Math. Helv. 47 (1972), 70-74. MR 46 #5310. MR 0306183 (46:5310)
  • [2] E. Matlis, The multiplicity and reduction number of a one-dimensional local ring, Proc. London Math. Soc. (3) 26 (1973), 273-288. MR 47 #1802. MR 0313247 (47:1802)
  • [3] N. H. McCoy, Rings and ideals, Carus Math. Monographs, no. 8, Open Court, LaSalle, Ill., 1948. MR 10, 96. MR 0026038 (10:96b)
  • [4] J. Sally and W. Vasconcelos, Stable rings, J. Pure Appl. Algebra 4 (1974), 319-336. MR 0409430 (53:13185)

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Keywords: Quasi-local ring, ideal, faithfully flat ring extension
Article copyright: © Copyright 1975 American Mathematical Society

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