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- Asma Ali, Basudeb Dhara, Shahoor Khan
- 2014

Let R be a prime ring with extended centroid C, F a generalized derivation of R and n ≥ 1, m ≥ 1 fixed integers. In this paper we study the situations: 1. (F (x • y)) m = (x • y) n for all x, y ∈ I, where I is a nonzero ideal of R; 2. (F (x • y)) n = (x • y) n for all x, y ∈ I, where I is a nonzero right ideal of R. Moreover, we also investigate the… (More)

Let R be a noncommutative prime ring with its Utumi ring of quotients U , C = Z(U) the extended centroid of R, F a generalized derivation of R and I a nonzero ideal of R. Suppose that there exists 0 = a ∈ R such that a(F ([x, y]) n − [x, y]) = 0 for all x, y ∈ I, where n ≥ 2 is a fixed integer. Then one of the following holds: 1. char (R) = 2, R ⊆ M 2 (C),… (More)

Let R be a prime ring of char R = 2, d a nonzero derivation of R, ρ a nonzero right ideal of R and 0 = b ∈ R such that b[[d 2 [x, y], [x, y]] n = 0 for all x, y ∈ ρ, n ≥ 1 fixed integer. If [ρ, ρ]ρ = 0 then either bρ = 0 or d(ρ)ρ = 0. Throughout this paper, R always denotes a prime ring with extended cen-troid C and Q its two sided Martindale ring of… (More)

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