( U,R) STRONGLY DERIVATION PAIRS ON LIE IDEALS IN RINGS

Abstract

Let R be an associative ring , U be a nonzero Lie ideal of R. In this paper , we will present the definition of (U,R) strongly derivation pair (d,g) , then we will get d=0 (resp. g=0 ) under  certain conditions on d and g for (U,R) strongly derivation pair (d,g) on semiprime ring . After that we will study prime rings , semiprime rings ,and rings  that have a commutator left nonzero divisor with (U,R) strongly derivation pair (d,g) , to obtain the notation of  (U,R) derivation .