Let R be a prime ring of characteristic different from 2, Q(r) its right Martindale quotient ring, L a non-central Lie ideal of R (i.e., L,R not equal 0), n >= 1 a fixed integer, F and G two generalized skew derivations of R, associated with the same automorphism alpha of R. If (F(xy)-G(x)y)(n) = 0, for any x,y is an element of L, then there exists a is an element of Q(r) such that , for any x is an element of R, unless when R satisfies the standard polynomial identity s(4)(x(1), ..., x(4)).
Certain functional identities involving a pair of generalized skew derivations with nilpotent values on Lie ideals
De Filippis, V;Scudo, G
2023-01-01
Abstract
Let R be a prime ring of characteristic different from 2, Q(r) its right Martindale quotient ring, L a non-central Lie ideal of R (i.e., L,R not equal 0), n >= 1 a fixed integer, F and G two generalized skew derivations of R, associated with the same automorphism alpha of R. If (F(xy)-G(x)y)(n) = 0, for any x,y is an element of L, then there exists a is an element of Q(r) such that , for any x is an element of R, unless when R satisfies the standard polynomial identity s(4)(x(1), ..., x(4)).File in questo prodotto:
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