Exploring the properties of the zero-divisor graph of direct product of $\ast$-rings

Document Type : Special Issue: First Joint IIIMT-Algebra Forum Conference 2023

Authors

1 School of Computational Sciences, Faculty of Science and Technology, JSPM University, Pune, India

2 Department of Mathematics, Aligarh Muslim University, Aligarh, India

Abstract

In this paper, we delve into the study of zero-divisor graphs in rings equipped with an involution. Specifically, we focus on abelian Rickart $\ast$-rings. Our investigation revolves around characterizing the diameter of a zero-divisor graph in the context of the direct product $\mathcal{S}_1 \oplus \mathcal{S}_2$, in relation to the diameters observed in the zero-divisor graphs of the constituent $\ast$-rings $\mathcal{S}_1$ and $\mathcal{S}_2$.

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References

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Journal of Mahani Mathematical Research
Volume 13, Issue 5 - Serial Number 30
Special Issue: First Joint IIIMT-Algebra Forum Conference 2023
December 2024
Pages 11-20

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History

  • Receive Date: 01 May 2024
  • Revise Date: 01 September 2024
  • Accept Date: 01 November 2024

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