Communications in Mathematics |

9486

Let R be a prime ring with center Z(R) and I a nonzero right ideal of R. Suppose that R admits a generalized reverse derivation (F, d) such that d(Z(R)) ≠ 0. In the present paper, we shall prove that if one of the following conditions holds: (i) F (xy) ± xy ∈ Z(R) (ii) F ([x, y]) ± [F (x), y] ∈ Z(R) (iii) F ([x, y]) ± [F (x), F (y)] ∈ Z(R) (iv) F (x ο y) ± F (x) ο F (y) ∈ Z(R) (v) [F (x), y] ± [x, F (y)] ∈ Z(R) (vi) F (x) ο y ± x ο F (y) ∈ Z(R) for all x, y ∈ I, then R is commutative.

Source: HAL:hal-03664963v1

Volume: Volume 27 (2019), Issue 1

Published on: July 4, 2019

Imported on: May 11, 2022

Keywords: General Mathematics,[MATH]Mathematics [math]

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