On Armendariz-like properties in Amalgamated algebras along ideals

N. Mahdou; A. Mimouni; M. elOuarrachi

On Armendariz-like properties in Amalgamated algebras along ideals

Commutative Algebra 2015-11-04 v1

Authors: N. Mahdou , A. Mimouni , M. elOuarrachi

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

Armendariz-like properties amalgamated algebras along ideals ring homomorphism Armendariz ring nil-Armendariz ring weak Armendariz ring transfer

Cite

@article{arxiv.1511.00788,
  title  = {On Armendariz-like properties in Amalgamated algebras along ideals},
  author = {N. Mahdou and A. Mimouni and M. elOuarrachi},
  journal= {arXiv preprint arXiv:1511.00788},
  year   = {2015}
}

On Armendariz-like properties in Amalgamated algebras along ideals

Abstract

Keywords

Cite

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