Title of article :
Examples of α-Skew π-Armendariz Rings
Author/Authors :
abduldaim, areej m. university of technology, branch of mathematics and computer applications - applied sciences department, iraq , ajaj, ahmed m. university of technology, branch of mathematics and computer applications - applied sciences department, iraq
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 :
α , skew , Armendariz rings , weak α , skew Armendariz , semicommutative ring , weak , rigid rings.
Journal title :
Iraqi Journal Of Science
Journal title :
Iraqi Journal Of Science
