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

Nazim, Mohd; Rehman, Nadeem Ur; Mir, Shabir Ahmad

doi:10.22103/jmmr.2024.23353.1639

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	Exploring the properties of the zero-divisor graph of direct product of $\ast$-rings
Journal of Mahani Mathematical Research
دوره 13، شماره 5 - شماره پیاپی 30، اسفند 2024، صفحه 11-20 اصل مقاله (469.49 K)
نوع مقاله: Special Issue: First Joint IIIMT-Algebra Forum Conference 2023
شناسه دیجیتال (DOI): 10.22103/jmmr.2024.23353.1639
نویسندگان
Mohd Nazim^* ¹؛ Nadeem Ur Rehman²؛ Shabir Ahmad Mir¹
¹School of Computational Sciences, Faculty of Science and Technology, JSPM University, Pune, India
²Department of Mathematics, Aligarh Muslim University, Aligarh, India
چکیده
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 $\mathcal{S}_2$.
کلیدواژه‌ها
$\ast$-ring؛ Rickart $\ast$-ring؛ zero-divisor graph

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