caa a22 4500 445869038 CHVBK 20180317145506.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00605-009-0179-y doi (NATIONALLICENCE)springer-10.1007/s00605-009-0179-y Liu Cheng-Kai Department of Mathematics, National Changhua University of Education, 500, Changhua, Taiwan aut Derivations cocentralizing multilinear polynomials on left ideals [Elektronische Daten] [Cheng-Kai Liu] Let R be a prime ring with extended centroid C, λ a nonzero left ideal of R and f (X 1, . . . , X t) a nonzero multilinear polynomial over C. Suppose that d and δ are derivations of R such that $$d(f(x_{1},\ldots,x_{t}))f(x_{1},\ldots,x_{t})-f(x_{1},\ldots,x_{t})\delta(f(x_{1},\ldots,x_{t}))\in C$$for all $${x_1,\ldots,x_t\in\lambda}$$. Then either d=0 and λ δ(λ)=0 or λ C=RCe for some idempotent e in the socle of RC and one of the following holds: (1)f (X1, . . . , Xt) is central-valued on eRCe;(2)λ(d + δ)(λ)=0 and f (X1, . . . , Xt)2 is central-valued on eRCe;(3)char R = 2 and eRCe satisfies st 4(X 1, X 2, X 3, X 4), the standard polynomial identity of degree 4. Springer-Verlag, 2010 Derivation nationallicence PI nationallicence GPI nationallicence Prime ring nationallicence Differential identity nationallicence Monatshefte für Mathematik Springer Vienna 162/3(2011-03-01), 297-311 0026-9255 162:3<297 2011 162 605 https://doi.org/10.1007/s00605-009-0179-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-009-0179-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Liu Cheng-Kai Department of Mathematics, National Changhua University of Education, 500, Changhua, Taiwan aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer Vienna 162/3(2011-03-01), 297-311 0026-9255 162:3<297 2011 162 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer