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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Powers of ideals generated by quadratic sequences

Author: K. Raghavan
Journal: Trans. Amer. Math. Soc. 343 (1994), 727-747
MSC: Primary 13C40; Secondary 13F50
MathSciNet review: 1188639
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Abstract: Huneke's conjecture that weak d-sequences generate ideals of quadratic type is proved. The proof suggests the definition of quadratic sequences, which are more general than weak d-sequences yet simpler to define and handle, in addition to being just as useful. We extend the theory of d-sequences and weak d-sequences to quadratic sequences. Results of Costa on sequences of linear type are generalized. An example of a two-dimensional local domain in which every system of parameters is a d-sequence in some order but which nevertheless fails to be Buchsbaum is given. A criterion is established for when equality holds in Burch's inequality for an ideal generated by a quadratic sequence.

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Keywords: d-sequence, weak d-sequence, quadratic sequence, relation type, Ratliff-Rush ideal, analytic deviation, Buchsbaum ring, Burch's inequality
Article copyright: © Copyright 1994 American Mathematical Society