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http://dx.doi.org/10.4134/CKMS.c200227

GENERALIZED DERIVATIONS ON PRIME RINGS SATISFYING CERTAIN IDENTITIES  

Al-Omary, Radwan Mohammed (Department of Mathematics Ibb University)
Nauman, Syed Khalid (Department of Mathematics Jinnah University for Women)
Publication Information
Communications of the Korean Mathematical Society / v.36, no.2, 2021 , pp. 229-238 More about this Journal
Abstract
Let R be a ring with characteristic different from 2. An additive mapping F : R → R is called a generalized derivation on R if there exists a derivation d : R → R such that F(xy) = F(x)y + xd(y) holds for all x, y ∈ R. In the present paper, we show that if R is a prime ring satisfying certain identities involving a generalized derivation F associated with a derivation d, then R becomes commutative and in some cases d comes out to be zero (i.e., F becomes a left centralizer). We provide some counter examples to justify that the restrictions imposed in the hypotheses of our theorems are not superfluous.
Keywords
Prime rings; derivations and generalized derivations; left centralizer;
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