• Corpus ID: 118669207

Three-Standardness of the Maximal Ideal

@article{Ananthnarayan2010ThreeStandardnessOT,
  title={Three-Standardness of the Maximal Ideal},
  author={H. Ananthnarayan and Craig Huneke},
  journal={arXiv: Commutative Algebra},
  year={2010}
}

• H. Ananthnarayan, C. Huneke
• Published 7 May 2010
• Mathematics
• arXiv: Commutative Algebra

We study a notion called $n$-standardness (defined by M. E. Rossi and extended in this paper) of ideals primary to the maximal ideal in a Cohen-Macaulay local ring and some of its consequences. We further study conditions under which the maximal ideal is three-standard, first proving results when the residue field has prime characteristic and then using the method of reduction to prime characteristic to extend the results to the equicharacteristic zero case. As an application, we extend a result due to T. Puthenpurakal and show that a certain length associated to a minimal reduction of the maximal ideal does not depend on the minimal reduction chosen.