Geodesic
Centralizing b-generalized derivations on multilinear polynomials
Filomat, Tome 33 (2019) no. 19, p. 6251

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DOI

Let R be a prime ring of characteristic different from 2 and F a b-generalized derivation on R. Let U be Utumi quotient ring of R with extended centroid C and f (x 1 ,. .. , x n) be a multilinear polynomial over C which is not central valued on R. Suppose that d is a non zero derivation on R such that d([F(f (r)), f (r)]) ∈ C for all r = (r 1 ,. .. , r n) ∈ R n ; then one of the following holds: (1) there exist a ∈ U, λ ∈ C such that F(x) = ax + λx + xa for all x ∈ R and f (x 1 ,. .. , x n) 2 is central valued on R, (2) there exists λ ∈ C such that F(x) = λx for all x ∈ R
DOI : 10.2298/FIL1919251T
Classification : 16N60, 16W25
Keywords: b-generalized derivations, multilinear polynomials, prime rings, extended centroid, Utumi quotient ring 
S K Tiwari; B Prajapati. Centralizing b-generalized derivations on multilinear polynomials. Filomat, Tome 33 (2019) no. 19, p. 6251 . doi: 10.2298/FIL1919251T
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     title = {Centralizing b-generalized derivations on multilinear polynomials},
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     year = {2019},
     volume = {33},
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     doi = {10.2298/FIL1919251T},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL1919251T/}
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