On Armendariz-like properties in Amalgamated algebras along ideals

2015/11/03 by Najib Mahdou, N. Mahdou, Mahdou, N. +4
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AC

paper · pdf · doi:10.48550/arxiv.1511.00788

arxiv created 2015/11/03 · openalex publication_date 2015/11/03 · arxiv updated 2015/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f: A→ 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.

Related

• Amalgamated algebras along an ideal
• Self injective property in amalgamated algebra along an ideal
• Prüfer-like conditions on an amalgamated algebra along an ideal
• Gaussian property in amalgamated algebras along an ideal
• Cohen-Macaulay and Gorenstein properties under the amalgamated construction