International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 4, Pages 813-816
Notes on -derivations
Adnan Menderes University, Faculty of Arts and Sciences, Department of Mathematics, Aydin 0910, Turkey
Received 18 December 1995; Revised 2 April 1996
Copyright © 1997 Neşet Aydin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a prime ring of characteristic not , a nonzero ideal of and -derivation of where and are automorphisms of . i) then ii) For ,
the following conditions are equivalent (I) , for all
or and (or ) for all
. Let be a -torsion free semiprime ring and be a nonzero ideal of iii) Let be a -derivation of and be a -derivation of . Suppose that is a -derivation and
commutes both and then , for all iv) Let and be an
-derivation of and be a -derivation of such that commutes both , and . If for all
, then is a -derivation on .