Authors: ABDESLAM MIMOUNI, NAJIB MAHDOU, MOUNIR EL OURRACHI
Abstract: 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.
Keywords: Amalgamated algebra along an ideal, reduced ring, Armendariz ring, nil-Armendariz ring, weak Armendariz, semicommutative ring
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