Open AccessGeneralized derivations vanishing on co-commutator identities in prime rings
Author(s) -
Basudeb Dhara
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2106785d
Subject(s) - mathematics , prime ring , commutator , noncommutative geometry , quotient , prime (order theory) , multilinear map , combinatorics , ideal (ethics) , quotient ring , ring (chemistry) , polynomial , centroid , polynomial ring , pure mathematics , discrete mathematics , algebra over a field , geometry , mathematical analysis , philosophy , chemistry , lie conformal algebra , organic chemistry , epistemology
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(? 0), 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]).