English

The $i$-extended ideal-based cozero-divisor graph of a commutative ring

Commutative Algebra 2026-05-08 v1

Abstract

Let R be a commutative ring with identity and let J be an ideal of R. In this paper, we introduce and investigate the notion of the i-extended ideal-based cozero-divisor graph of R. This graph, denoted by ΓJi(R)\overline{\Gamma''}_{Ji}(R), is a simple graph of R whose vertex set is xR J:xR+JR{x \in R \ J : xR + J \not= R}. Two distinct vertices xx and yy are adjacent if and only if xm∉ynR+Jx^m \not \in y^nR+J and yn∉xmR+Jy^n \not \in x^mR+J for some positive integers m and n with nin\leq i and mim\leq i.

Keywords

Cite

@article{arxiv.2605.05237,
  title  = {The $i$-extended ideal-based cozero-divisor graph of a commutative ring},
  author = {Faranak Farshadifar},
  journal= {arXiv preprint arXiv:2605.05237},
  year   = {2026}
}
R2 v1 2026-07-01T12:53:21.922Z