Zero-divisor graphs of amalgamations

  • Salah-Eddine Kabbaj
  • Abdeslam Mimouni

Abstract

Let $f\colon A\rightarrow B$ be a homomorphism of commutative rings and let $J$ be an ideal of $B$. The amalgamation of $A$ with $B$ along $J$ with respect to $f$ is the subring of $A\times B$ given by \[ A\bowtie ^{f}J:=\{(a,f(a)+j) \mid a\in A, j\in J\}. \] This paper investigates the zero-divisor graph of amalgamations. Our aim is to characterize when the graph is complete and compute its diameter and girth for various contexts of amalgamations. The new results recover well-known results on duplications, and yield new and original examples issued from amalgamations.

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Published
2018-09-05
How to Cite
Kabbaj, S.-E., & Mimouni, A. (2018). Zero-divisor graphs of amalgamations. MATHEMATICA SCANDINAVICA, 123(2), 174-190. https://doi.org/10.7146/math.scand.a-105307
Section
Articles