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

We investigate some properties of generalized (a,b)-derivations on semiprime rings. Among some other results, we show that if g is a generalized (a,b)-derivation, with associated (a,b)-derivation d, on a semiprime ring R such that [g(x),a(x)]=0 for all x\in R, then d(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 (a,b)-derivation g, with associated (a,b)-derivation d, such that g([m(x),w(y)])=[n(x),w(y)]a,t, where w:R\rightarrow R is commutativity preserving, then [y,z]d(w(p))=0 for all y,z,p\in R.

Anahtar Kelimeler:

Semiprime ring, derivation, generalized derivation, generalized (a, b)-derivation

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

Keywords:

Semiprime ring, derivation, generalized derivation, generalized (a, b)-derivation,

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Centre for Advanced Studies in Pure and Applied Mathematics Bahauddin Zakariya University Multan-PAKISTAN e-mail: faisalali@bzu.edu.pk Muhammad Anwar CHAUDHRY Centre for Advanced Studies in Pure and Applied Mathematics Bahauddin Zakariya University Multan-PAKISTAN e-mail: chaudhry@bzu.edu.pk