Let $f: A\rightarrow B$ be a ring homomorphism and $J$ be an ideal of $B$. In this paper, we investigate the transfer of Armendariz-like properties to the amalgamation of $A$ with $B$ along $J$ with respect to $f$ (denoted by $A\bowtie^fJ)$ introduced and studied by D'Anna, Finocchiaro, and Fontana in 2009. Our aim is to provide necessary and sufficient conditions for $A\bowtie^fJ$ to be an Armendariz ring, nil-Armendariz ring, and weak Armendariz ring.
Amalgamated algebra along an ideal, reduced ring, Armendariz ring, nil-Armendariz ring, weak Armendariz, semicommutative ring
MIMOUNI, ABDESLAM; MAHDOU, NAJIB; and OURRACHI, MOUNIR EL
"On Armendariz-like properties in amalgamated algebras along ideals,"
Turkish Journal of Mathematics: Vol. 41:
6, Article 24.
Available at: https://journals.tubitak.gov.tr/math/vol41/iss6/24