Generalized derivations of prime rings on multilinear polynomials with annihilator conditions

Authors : Nurcan ARGAÇ, Çağrı DEMİR

Pages : 231-243

Doi:10.3906/mat-1106-46

View : 10 | Download : 7

Publication Date : 0000-00-00

Article Type : Research Paper

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 finsert ignore into journalissuearticles values(X1,..., Xn); a multilinear polynomial over K. If aginsert ignore into journalissuearticles values(finsert ignore into journalissuearticles values(x1,...,xn););finsert ignore into journalissuearticles values(x1,...,xn);=0 for all x1,...,xn \in I, then one of the following holds: insert ignore into journalissuearticles values(1); aI=aginsert ignore into journalissuearticles values(I);=0; insert ignore into journalissuearticles values(2); ginsert ignore into journalissuearticles values(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=ainsert ignore into journalissuearticles values(b+c);I; insert ignore into journalissuearticles values(3); [finsert ignore into journalissuearticles values(X1,...,Xn);,Xn+1]Xn+2 is an identity for I.
Keywords : Prime ring, derivation, generalized derivation, right Utumi quotient ring, differential identity, generalized polynomial identity