Turkish Journal of Mathematics
DOI
10.3906/mat-1106-46
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.
Keywords
Prime ring, derivation, generalized derivation, right Utumi quotient ring, differential identity, generalized polynomial identity
First Page
231
Last Page
243
Recommended Citation
ARGAÇ, NURCAN and DEMİR, ÇAĞRI
(2013)
"Generalized derivations of prime rings on multilinear polynomials with annihilator conditions,"
Turkish Journal of Mathematics: Vol. 37:
No.
2, Article 5.
https://doi.org/10.3906/mat-1106-46
Available at:
https://journals.tubitak.gov.tr/math/vol37/iss2/5
