Centralizing automorphisms and Jordan left derivations on $σ$-prime rings

Details Centralizing automorphisms and Jordan left derivations on $σ$-prime rings Centralizing automorphisms and Jordan left derivations on $σ$-prime rings

2009-02-04

arxiv.org/abs/0902.0815v1

Advances in algebra 1 (1) (2008) 19-26

Mathematics

Rings and Algebras

8 pages

Scientific paper

Let $R$ be a 2-torsion free $\sigma$-prime ring. It is shown here that if $U\not\subset Z(R)$ is a $\sigma$-Lie ideal of $R$ and $a, b$ in $R$ such that $aUb=\sigma(a)Ub=0,$ then either $a=0$ or $b=0.$ This result is then applied to study the relationship between the structure of $R$ and certain automorphisms on $R$. To end this paper, we describe additive maps $d: R \longrightarrow R$ such that $d(u^2) = 2ud(u)$ where $u\in U,$ a nonzero $\sigma$-square closed Lie ideal of $R.$

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