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PreprintCC BY 4.0arXiv

A lower bound on depth A/In

  • Tony J. Puthenpurakal
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Abstract

Let (A,m) be a Noetherian local ring and let I⊆ m be an ideal in A. Let ℓ(I) be the analytic spread of I. Let GI(A) = ⨁n ≥ 0In/In+1 be the associated graded ring of I and let its depth be t. We prove depth A/In ≥ t − ℓ(I) for all n≥ 1.

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Cite

BibTeXRIS
BibTeX
@misc{puthenpurakal2026lower,
  title = {{A lower bound on $\textdepth \ \mathbfA/I^n$}},
  author = {Tony J. Puthenpurakal},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.14973},
  eprint = {2610.14973},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.14973},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A lower bound on depth A/I^n
AU  - Tony J. Puthenpurakal
PY  - 2026
DA  - 2026/10/10
PB  - arXiv
DO  - 10.48550/arxiv.2610.14973
UR  - https://arxiv.org/abs/2610.14973
AB  - Let (A,m) be a Noetherian local ring and let I⊆ m be an ideal in A. Let ℓ(I) be the analytic spread of I. Let G_I(A) = ⨁_n ≥ 0I^n/I^n+1 be the associated graded ring of I and let its depth be t. We prove depth A/I^n ≥ t − ℓ(I) for all n≥ 1.
ER  -