%0 Journal Article
%T Dependent Elements in Prime and Semiprime Gamma Rings
%A Kalyan Kumar Dey
%A Akhil Chandra Paul
%A Isamiddin S. Rakhimov
%J Asian Journal of Algebra
%D 2012
%I 
%X Let M be a ¦£-ring. An element a¡ÊM is called a dependent element on a mapping F: M¡úM if F(x)¦Áa = a¦Áx holds for all x¡ÊM, a¡Ê¦£. In this study, we determine the characterizations of dependent elements on certain mappings on prime and semiprime ¦£-rings by taking a certain assumption x¦Áy¦Âz = x¦Ây¦Áz for all x,y,z¡ÊM, ¦Á¦Â¡Ê¦£. For the case of semiprime ¦£-ring M, we also prove that the mapping s+t is a free action if s and t are automorphisms of M.
%K Derivation
%K free action
%U http://docsdrive.com/pdfs/ansinet/aja/2012/11-20.pdf