Some Results for Endomorphisms in Prime Rings

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Authors: A. BOUA

DOI: 10.46793/KgJMat2106.943B


In this article, we present some commutativity theorems for a prime ring equipped with endomorphisms α, β, γ and δ satisfying any one of the following identities:

  1. [α(x)(y)] + γ([x,y]) + δ(x y) = 0 for all x,y ∈ℛ;
  2. α(x) β(y) + γ([x,y]) = 0 for all x,y ∈ℛ.

Moreover, we provide examples to show that the assumed restrictions cannot be relaxed.


Prime ring, endomorphisms, commutativity.


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