Some Results for Endomorphisms in Prime Rings
Download PDF
Authors: A. BOUA
DOI: 10.46793/KgJMat2106.943B
Abstract:
In this article, we present some commutativity theorems for a prime ring ℛ equipped with endomorphisms α, β, γ and δ satisfying any one of the following identities:
- [α(x),β(y)] + γ([x,y]) + δ(x ∘ y) = 0 for all x,y ∈ℛ;
- 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.
Keywords:
Prime ring, endomorphisms, commutativity.
References:
[1] M. Ashraf, A. Ali and S. Ali, (σ,τ)-derivations on prime near rings, Arch. Math. 40(3) (2004), 281–286.
[2] M. Ashraf and N. Rehman, On commutativity of rings with derivations, Results Math. 42(1–2) (2002), 3–8.
[3] M. Ashraf and A. Boua, On semiderivations in 3-prime near-rings, Commun. Korean Math. Soc. 31(3) (2016), 433–445.
[4] H. E. Bell and M. N. Daif, On commutativity and strong commutativity preserving maps, Canad. Math. Bull. 37 (1994), 443–447.
[5] H. E. Bell and N.-Ur Rehman, Generalized derivations with commutativity and anti-commutativity conditions, Math. J. Okayama Univ. 49 (2007), 139–147.
[6] M. Bresar, On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J. 33 (1991), 89–93.
[7] A. A. Klein, A new proof of a result of Levitzki, Proc. Amer. Math. Soc. 81(1) (1981), 8.
Login:
