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

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}_۱ \oplus \mathcal{S}_۲, in relation to the diameters observed in the zero-divisor graphs of the constituent \ast-rings \mathcal{S}_۱ and \mathcal{S}_۲.

کلیدواژه ها:

\ast-ring ، Rickart \ast-ring ، zero-divisor graph