Turkish Journal of Mathematics
Abstract
Let K be a commutative ring with unity, R be a prime K-algebra with characteristic not 2, U be the right Utumi quotient ring of R, C the extended centroid of R, I a nonzero right ideal of R and a a fixed element of R. Let g be a generalized derivation of R and f(X_1,..., X_n) a multilinear polynomial over K. If ag(f(x_1,...,x_n))f(x_1,...,x_n)=0 for all x_1,...,x_n \in I, then one of the following holds: (1) aI=ag(I)=0; (2) g(x)=bx+[c,x] for all x\in R, where b,c\in U. In this case either [c,I]I=0=abI or aI=0=a(b+c)I; (3) [f(X_1,...,X_n),X_{n+1}]X_{n+2} is an identity for I.
DOI
10.3906/mat-1106-46
Keywords
Prime ring, derivation, generalized derivation, right Utumi quotient ring, differential identity, generalized polynomial identity
First Page
231
Last Page
243
Recommended Citation
ARGAÇ, N, & DEMİR, Ç (2013). Generalized derivations of prime rings on multilinear polynomials with annihilator conditions. Turkish Journal of Mathematics 37 (2): 231-243. https://doi.org/10.3906/mat-1106-46
