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Characterizing Jordan Higher Centralizers on Triangular Rings through Zero Product | ||
| Iraqi Journal of Science | ||
| Article 1, Volume 56, Issue 3, 2015, Pages 2648-2653 | ||
| Authors | ||
| ; Rajaa C.Shaheen | ||
| Abstract | ||
| In this paper , we prove that if T is a 2-torsion free triangular ring and φ=〖(φ_i)〗_(i∈N) be a family of additive mapping 〖 φ〗_i:T→T then φ satisfying Xφ_i (Y)+φ_i (Y)X=0 ∀ i∈N whenever X,Y∈T,XY=YX=0 ifand only if φ is a higher centralizer which is means that φ is Jordan higher centralizer on 2-torsion free triangular ring if and only if φ is a higher centralizer and also we prove that if φ=〖(φ_i)〗_(i∈N) be a family of additive mapping φ_i:T→T satisfying the relation φ_n (XYX)=∑_(i=1)^n▒X φ_i (Y)X ∀ X,Y∈T, Then φ is a higher centralizer. | ||
| Keywords | ||
| higher centralizer; Jordan higher centralizer | ||
|
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