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Examples of α-Skew π-Armendariz Rings | ||
| Iraqi Journal of Science | ||
| Article 1, Volume 58, Issue 1, 2018, Pages 482-489 | ||
| Authors | ||
| Areej M. Abduldaim; Ahmed M. Ajaj | ||
| Abstract | ||
| In this paper extensive examples and related counterexamples of the category of α-skew π-Armendariz rings are given. This category of rings regards a new generalization for the concepts of α-skew Armendariz and skew π-Armendariz rings. A ring Α is called α-skew π-Armendariz if for any φ(χ)=∑_(z=0)^λ▒〖ι_z χ^z 〗 and ψ(χ)=∑_(s=0)^μ▒〖ν_s χ^s 〗∈Α[χ;α] such that φ(χ)ψ(χ)∈N(Α[χ;α]), then ι_z α^z (ν_s)∈N(Α) for each 0≤z≤λ and 0≤s≤μ. First some general properties of α-skew π-Armendariz rings are studied and then relations between α-skew π-Armendariz rings and other related rings are investigated. Also various examples of non α-skew π-Armendariz rings are established. | ||
| Keywords | ||
| Skew | ||
|
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