Structure of (σ, ρ)-n-Derivations on Rings

Authors

  • Abu Zaid Ansari Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, KSA https://orcid.org/0000-0001-6139-7521
  • Faiza Shujat Department of Mathematics, Faculty of Science, Taibah University, Madinah, KSA
  • Ahlam Fallatah Department of Mathematics, Faculty of Science, Taibah University, Madinah, KSA

DOI:

https://doi.org/10.37256/cm.5420245144

Keywords:

prime ring, (σ, ρ)-derivation, Jordan n-derivation, ∗-n-centralizers

Abstract

The goal of this research is to describe the structure of Jordan (σ, ρ)-n-derivations on a prime ring. By (σ, ρ)- n-derivations, we mean n-additive maps ℑ : Rn R  satisfying the following property in each n-slot:

                  ℑ(pq, ϖ1, ··· , ϖn1) = ℑ(p, ϖ1, ··· , ϖn1)σ(q) +ρ(p)ℑ(q, ϖ1, ··· , ϖn1),

for every p, q, ϖ1, ··· , ϖn1R. We find the conditions under which every Jordan (σ, ρ)-n-derivation becomes a (σ, ρ)-n-derivation. Moreover, the concept of -n-centralizers on -ring has given. The -ring is also used for examining some outcomes, where left and right -n-centralizers are significant

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Published

2024-11-29

How to Cite

1.
Ansari AZ, Shujat F, Fallatah A. Structure of (<i>σ, ρ</i>)-<i>n</i>-Derivations on Rings. Contemp. Math. [Internet]. 2024 Nov. 29 [cited 2024 Dec. 4];5(4):5666-78. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/5144