- Turkish Journal of Mathematics
- Vol: 41 Issue: 6
- On Armendariz-like properties in amalgamated algebras along ideals
On Armendariz-like properties in amalgamated algebras along ideals
Authors : Abdeslam Mimouni, Najib Mahdou, Mounir El Ourrachi
Pages : 1673-1686
View : 8 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
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