Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1603-135
Keywords
Amalgamated algebra along an ideal, reduced ring, Armendariz ring, nil-Armendariz ring, weak Armendariz, semicommutative ring
First Page
1673
Last Page
1686
Recommended Citation
MIMOUNI, A, MAHDOU, N, & OURRACHI, M. E (2017). On Armendariz-like properties in amalgamated algebras along ideals. Turkish Journal of Mathematics 41 (6): 1673-1686. https://doi.org/10.3906/mat-1603-135
