caa a22 4500 445868759 CHVBK 20180317145505.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s00605-010-0231-y doi (NATIONALLICENCE)springer-10.1007/s00605-010-0231-y Certain additive maps on m -power closed Lie ideals [Elektronische Daten] [Tsiu-Kwen Lee, Kun-Shan Liu] Let R be a prime ring with extended centroid C and m a fixed positive integer >1. A Lie ideal L of R is called m-power closed if $${u^m \in L}$$ for all $${u \in L}$$ . We prove that if char R = 0 or a prime p>m, then every non-central, m-power closed Lie ideal L of R contains a nonzero ideal of R except when dimC RC=4, m is odd, and $${u^{m-1} \in C}$$ for all $${u \in L}$$ . Moreover, the additive maps d : L → R satisfying d(u m)=mu m-1 d(u) (resp. d(u m)=u m-1 d(u)) for all $${u \in L}$$ are completely characterized if char R = 0 or a prime p>2(m − 1). Springer-Verlag, 2010 Prime ring nationallicence m -Power closed Lie ideal nationallicence Additive map nationallicence PI nationallicence GPI nationallicence Functional identity nationallicence Lee Tsiu-Kwen Department of Mathematics, National Taiwan University, 106, Taipei, Taiwan aut Liu Kun-Shan Department of Mathematics, National Taiwan University, 106, Taipei, Taiwan aut Monatshefte für Mathematik Springer Vienna 164/3(2011-11-01), 287-298 0026-9255 164:3<287 2011 164 605 https://doi.org/10.1007/s00605-010-0231-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-010-0231-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lee Tsiu-Kwen Department of Mathematics, National Taiwan University, 106, Taipei, Taiwan aut NATIONALLICENCE 700 1- Liu Kun-Shan Department of Mathematics, National Taiwan University, 106, Taipei, Taiwan aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer Vienna 164/3(2011-11-01), 287-298 0026-9255 164:3<287 2011 164 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer