Year: 2026
Type: preprint
Abstract: We construct a family of finite local rings whose annihilating-ideal graphs are naturally described by orthogonality of subspaces of $\mathbb{F}_2^n$. For $n=4$ we determine the clique and chromatic numbers exactly and obtain \[ ω(\AG(R_4))=5<6=χ(\AG(R_4)). \] Thus $\AG(R_4)$ is not weakly perfect, and the Behboodi--Rakeei conjecture fails for non-reduced commutative rings.
Source: arXiv (Cornell University)
Author: Nikandish, R.
Institution: Jundi-Shapur University of Technology
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214045826
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