On Armendariz-like properties in Amalgamated algebras along ideals

Abstract

Let $f:A\to B$ 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 $A{\bowtie }^{f}J)$ introduced and studied by D'Anna, Finocchiaro and Fontana in 2009. Our aim is to provide necessary and sufficient conditions for $A{\bowtie }^{f}J,$ to be an Armendariz ring, nil-Armendariz ring and weak Armendariz ring.

References in corpus (1)

• The amalgamated duplication of a ring along a multiplicative-canonical ideal