On generalized (a,b)-derivations of semiprime rings

Authors : Faisal ALİ

Pages : 399-404

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :We investigate some properties of generalized insert ignore into journalissuearticles values(a,b);-derivations on semiprime rings. Among some other results, we show that if g is a generalized insert ignore into journalissuearticles values(a,b);-derivation, with associated insert ignore into journalissuearticles values(a,b);-derivation d, on a semiprime ring R such that [ginsert ignore into journalissuearticles values(x);,ainsert ignore into journalissuearticles values(x);]=0 for all x\in R, then dinsert ignore into journalissuearticles values(x);[y,z]=0 for all x,y,z\in R and d is central. We also show that if a,n,t are endomorphisms and b,m are automorphisms of a semiprime ring R and if R has a generalized insert ignore into journalissuearticles values(a,b);-derivation g, with associated insert ignore into journalissuearticles values(a,b);-derivation d, such that ginsert ignore into journalissuearticles values([minsert ignore into journalissuearticles values(x);,winsert ignore into journalissuearticles values(y);]);=[ninsert ignore into journalissuearticles values(x);,winsert ignore into journalissuearticles values(y);]a,t, where w:R\rightarrow R is commutativity preserving, then [y,z]dinsert ignore into journalissuearticles values(winsert ignore into journalissuearticles values(p););=0 for all y,z,p\in R.
Keywords : Semiprime ring, derivation, generalized derivation, generalized a, b, derivation