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PreprintCC BY 4.0arXiv

Annihilating-Ideal Graphs and Orthogonality Graphs over 𝔽2

  • R. Nikandish
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Abstract

We construct a family of finite local rings whose annihilating-ideal graphs are naturally described by orthogonality of subspaces of 𝔽2n. For n=4 we determine the clique and chromatic numbers exactly and obtain Ο‰(AG(R4))=5<6=Ο‡(AG(R4)). Thus AG(R4) is not weakly perfect, and the Behboodi--Rakeei conjecture fails for non-reduced commutative rings.

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Cite

BibTeXRIS
BibTeX
@misc{nikandish2026annihilatingideal,
  title = {{Annihilating-Ideal Graphs and Orthogonality Graphs over $\mathbbF_2$}},
  author = {R. Nikandish},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22769},
  eprint = {2609.22769},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22769},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Annihilating-Ideal Graphs and Orthogonality Graphs over 𝔽_2
AU  - R. Nikandish
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.22769
UR  - https://arxiv.org/abs/2609.22769
AB  - We construct a family of finite local rings whose annihilating-ideal graphs are naturally described by orthogonality of subspaces of 𝔽_2^n. For n=4 we determine the clique and chromatic numbers exactly and obtain Ο‰(AG(R_4))=5<6=Ο‡(AG(R_4)). Thus AG(R_4) is not weakly perfect, and the Behboodi--Rakeei conjecture fails for non-reduced commutative rings.
ER  -