Annihilators and Power Values of Generalized Skew Derivations on Lie Ideals

Filippis, Vincenzo De

Canadian mathematical bulletin, Tome 59 (2016) no. 2, pp. 258-270

Résumé

Let $R$ be a prime ring of characteristic diòerent from $2$ , let ${{Q}_{r}}$ be its right Martindale quotient ring, and let $C$ be its extended centroid. Suppose that $F$ is a generalized skew derivation of $R,\,L$ a non-central Lie ideal of $R,\,0\,\ne \,a\,\in \,R,\,m\,\ge \,0$ and $n,\,s\,\ge \,1$ fixed integers. If $$a{{\left( {{u}^{m}}F\left( u \right){{u}^{n}} \right)}^{s}}\,=\,0$$ for all $u\,\in \,L$ , then either $R\,\subseteq \,{{M}_{2}}\left( C \right)$ , the ring of $2\,\times \,2$ matrices over $C$ , or $m\,=\,0$ and there exists $b\,\in \,{{Q}_{r}}$ such that $F\left( x \right)\,=\,bx$ , for any $x\,\in \,R$ , with $ab\,=\,0$ .

Détail

DOI : 10.4153/CMB-2015-077-x

Mots-clés : 16W25, 16N60, generalized skew derivation, prime ring

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