Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 2 min ago
PreprintarXiv licencearXiv

Some Remarks on Regular Sequences and Complete Intersections

  • Manolis C. Tsakiris
Open at sourcePDFDOICite

Abstract

We give an ideal in a polynomial ring in three variables, generated by three elements and having height equal to three, but for which no permutation of its generators is a regular sequence. We prove that in a polynomial ring over an infinite field, an ideal of height n generated by n polynomials, always admits a set of n generators, for which any permutation is a regular sequence.

Related

  1. Some remarks on Talagrand's convolution conjecture
    Alexander Shaposhnikov
    arXivPreprintarXiv licenceFull textAnalysis & PDEsProbabilityarXiv
  2. Some remarks on realizations defining diagrammatic Hecke categories
    Amit Hazi
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Some remarks on polynomial vector fields in RR2
    Supriyo Jana, Soumen Sarkar
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv
  4. Some remarks on the moment method for null controllability of parabolic equations in any dimension
    Morgan Morancey
    HALPreprintCC BY-NC-SA 4.0Full textOptimisation & controlHAL
  5. Some remarks on nonexistence in the Gamow liquid drop model
    Dario Mazzoleni, Aldo Pratelli, Berardo Ruffini
    arXivPreprintarXiv licenceFull textAnalysis & PDEsOptimisation & controlarXiv

Cite

BibTeXRIS
BibTeX
@misc{tsakiris2026some,
  title = {{Some Remarks on Regular Sequences and Complete Intersections}},
  author = {Manolis C. Tsakiris},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15261},
  eprint = {2610.15261},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15261},
}
RIS
TY  - UNPB
TI  - Some Remarks on Regular Sequences and Complete Intersections
AU  - Manolis C. Tsakiris
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.15261
UR  - https://arxiv.org/abs/2610.15261
AB  - We give an ideal in a polynomial ring in three variables, generated by three elements and having height equal to three, but for which no permutation of its generators is a regular sequence. We prove that in a polynomial ring over an infinite field, an ideal of height n generated by n polynomials, always admits a set of n generators, for which any permutation is a regular sequence.
ER  -