Shuliang Huang - Generalized reverse derivations and commutativity of prime rings

cm:9486 - Communications in Mathematics, July 4, 2019, Volume 27 (2019), Issue 1 - https://doi.org/10.2478/cm-2019-0004
Generalized reverse derivations and commutativity of prime rings

Authors: Shuliang Huang

    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.


    Volume: Volume 27 (2019), Issue 1
    Published on: July 4, 2019
    Imported on: May 11, 2022
    Keywords: General Mathematics,[MATH]Mathematics [math]

    1 Document citing this article

    Consultation statistics

    This page has been seen 87 times.
    This article's PDF has been downloaded 47 times.