TY - JOUR
AU - Salah-Eddine Kabbaj
AU - Abdeslam Mimouni
PY - 2018/09/05
Y2 - 2018/12/14
TI - Zero-divisor graphs of amalgamations
JF - MATHEMATICA SCANDINAVICA
JA - MathScand
VL - 123
IS - 2
SE - Articles
DO - 10.7146/math.scand.a-105307
UR - https://www.mscand.dk/article/view/105307
AB - 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.
ER -