Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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RINGS WHOSE ASSOCIATED EXTENDED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED

  • Driss Bennis (Department of Mathematics Faculty of Sciences Mohammed V University in Rabat) ;
  • Brahim El Alaoui (Department of Mathematics Faculty of Sciences Mohammed V University in Rabat) ;
  • Raja L'hamri (Department of Mathematics Faculty of Sciences Mohammed V University in Rabat)
  • Received : 2023.06.12
  • Accepted : 2023.10.05
  • Published : 2024.05.31
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Abstract

Let R be a commutative ring with identity 1≠ 0. In this paper, we continue the study started in [10] to further investigate when the extended zero-divisor graph of R, denoted as $\bar{\Gamma}$(R), is complemented. We also study when $\bar{\Gamma}$(R) is uniquely complemented. We give a complete characterization of when $\bar{\Gamma}$(R) of a finite ring R is complemented. Various examples are given using the direct product of rings and idealizations of modules.

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Acknowledgement

The authors would like to express their gratitude to the referee for the meticulous review of the paper and for providing valuable suggestions that have enhanced the quality of this paper.

References

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