English

Some results on the ideal-based cozero-divisor graph of a commutative ring

Commutative Algebra 2025-10-24 v2

Abstract

Let R be a commutative ring with identity and I be an ideal of R. The cozero-divisor graph with respect to I, denoted by ΓI(R)\Gamma''_I(R), is the graph of R with vertices {x \in R -I :xR +I \not=R} and two distinct vertices xx and yy are adjacent if and only if x∉yR+Ix \not \in yR+I and y∉xR+Iy \not \in xR+I.In this paper, we obtained some results on ΓI(R)\Gamma''_I(R).

Keywords

Cite

@article{arxiv.2508.13222,
  title  = {Some results on the ideal-based cozero-divisor graph of a commutative ring},
  author = {F. Farshadifar},
  journal= {arXiv preprint arXiv:2508.13222},
  year   = {2025}
}