Geodesic
Generalized derivations vanishing on Co-Commutator identities in prime rings
Filomat, Tome 35 (2021) no. 6, p. 1785

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DOI

Let R be a noncommutative prime ring of char (R) , 2 with Utumi quotient ring U and extended centroid C and I a nonzero two sided ideal of R. Suppose that F(ǂ0), G and H are three generalized derivations of R and f (x1, . . . , xn) is a multilinear polynomial over C, which is not central valued on R. If F(G( f (r)) f (r) − f (r)H( f (r))) = 0 for all r = (r1, . . . , rn) ∈ Iⁿ, then we obtain information about the structure of R and describe the all possible forms of the maps F, G and H. This result generalizes many known results recently proved by several authors ([1], [4], [5], [8], [9], [13], [15]).
DOI : 10.2298/FIL2106785D
Classification : 16W25, 16N60
Keywords: Prime ring, derivation, generalized derivation, extended centroid, Utumi quotient ring 
Basudeb Dhara. Generalized derivations vanishing on Co-Commutator identities in prime rings. Filomat, Tome 35 (2021) no. 6, p. 1785 . doi: 10.2298/FIL2106785D
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     author = {Basudeb Dhara},
     title = {Generalized derivations vanishing on {Co-Commutator} identities in prime rings},
     journal = {Filomat},
     pages = {1785 },
     year = {2021},
     volume = {35},
     number = {6},
     doi = {10.2298/FIL2106785D},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2106785D/}
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