Abstract
Let R and S be commutative rings with identity, \(f:R\rightarrow S\) a ring homomorphism and J an ideal of S. Then the subring \(R\bowtie ^fJ:=\{(r,f(r)+j)\mid r\in R\) and \(j\in J\}\) of \(R\times S\) is called the amalgamation of R with S along J with respect to f. In this paper, we generalize and improve recent results on the computation of the diameter of the zero-divisor graph of amalgamated algebras and obtain new results. In particular, we provide new characterizations for completeness of the zero-divisor graph of amalgamated algebra, as well as, a complete description for the diameter of the zero-divisor graph of amalgamations in the special case of finite rings.
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This research was in part supported by a Grant from IPM (No.991300116).
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Azimi, Y., Doustimehr, M.R. The zero-divisor graph of an amalgamated algebra. Rend. Circ. Mat. Palermo, II. Ser 70, 1213–1225 (2021). https://doi.org/10.1007/s12215-020-00554-x
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DOI: https://doi.org/10.1007/s12215-020-00554-x