Generalized derivations of prime rings on multilinear polynomials with annihilator conditions
Articles > Article · 2013
Authors: Nurcan ARGAÇ, Çağrı DEMİR
TURKISH JOURNAL OF MATHEMATICS, Journal Indexed in SCI Expanded, International, 2013, vol 37, pp 231-243
DOI: 10.3906/mat-1106-46
Summary
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 x1,..., x(n) is an element of I, then one of the following holds: