On Armendariz-like properties in amalgamated algebras along ideals

Authors : Abdeslam MIMOUNI, Najib MAHDOU, Mounir El OURRACHI

Pages : 1673-1686

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Publication Date : 0000-00-00

Article Type : Research Paper

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 $f$ insert ignore into journalissuearticles values(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