Commutativity conditions on derivations and Lie ideals $σ$-prime rings

Details Commutativity conditions on derivations and Lie ideals $σ$-prime rings Commutativity conditions on derivations and Lie ideals $σ$-prime rings

2009-07-14

arxiv.org/abs/0907.2266v1

Mathematics

Rings and Algebras

9 pages

Scientific paper

Let $R$ be a 2-torsion free $\sigma$-prime ring, $U$ a nonzero square closed $\sigma$-Lie ideal of $R$ and let $d$ be a derivation of $R$. In this paper it is shown that: 1) If $d$ is centralizing on $U$, then $d = 0$ or $U \subseteq Z(R)$. 2) If either $d([x, y]) = 0$ for all $x, y \in U$, or $[d(x), d(y)] = 0$ for all $x, y \in U$ and $d$ commutes with $\sigma$ on $U$, then $d = 0$ or $U \subseteq Z(R)$.

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