Resumen de Zero-divisor graphs of amalgamations

Salah-Eddine Kabbaj, Abdeslam Mimouni

• Letf:A→Bbe a homomorphism of commutative rings and letJbe an ideal ofB.TheamalgamationofAwithBalongJwith respect tofis the subring ofA×Bgiven by AfJ:={(a, f (a)+j)|a∈A, j∈J}.

  This paper investigates the zero-divisor graph of amalgamations. Our aim is to characterize whenthe 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 examplesissued from amalgamations.