## Powers of ideals generated by quadratic sequences

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- by K. Raghavan
- Trans. Amer. Math. Soc.
**343**(1994), 727-747 - DOI: https://doi.org/10.1090/S0002-9947-1994-1188639-1
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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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## Bibliographic Information

- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**343**(1994), 727-747 - MSC: Primary 13C40; Secondary 13F50
- DOI: https://doi.org/10.1090/S0002-9947-1994-1188639-1
- MathSciNet review: 1188639