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Zbl 1030.16022
Nadeem-ur-Rehman
On commutativity of rings with generalized derivations. (English)
[J] Math. J. Okayama Univ. 44, 43-49 (2002). ISSN 0030-1566

An additive map $F$ from a ring $R$ into itself is said to be a generalized derivation if there is a derivation $d$ of $R$ such that $F(xy)=F(x)y+xd(y)$ for all $x,y\in R$. The author extends some results that are known for derivations on prime rings to generalized derivations. The main results treat the conditions: (i) $[F(x),x]=0$, (ii) $F(xy-yx)=xy-yx$, and (iii) $F(xy+zy)=xy+yx$ for all $x$, $y$ in some appropriate subset of $R$.
[M.Brešar (Maribor)]

MSC 2000:: *16W25 Derivations, actions of Lie algebras (assoc. rings and algebras)
16N60 Prime and semiprime assoc. rings
16U70 Commutativity theorems for assoc. rings
16U80 Generalizations of commutativity (assoc. rings and algebras)
16R50 Other kinds of identities of assoc. rings

Keywords: commutativity theorems; commutator constraints; additive maps; prime rings; generalized derivations

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