SOME RESULTS OF GENERALIZED LEFT (θ,θ)-DERIVATIONS ON SEMIPRIME RINGS

Let R be an associative ring with center Z(R) . In this paper , we study the commutativity of semiprime rings under certain conditions , it comes through introduce the definition of generalized left(θ,θ)- derivation associated with left (θ,θ) -derivation , where Î¸ is a mapping on R

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

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

Commutativity of Addition in Prime Near-Rings with Right (θ,θ)-3-Derivations

Let N be a near-ring and  is a mapping on N . In this paper we introduce the notion of right ()-3-derivation in near-ring N. Also, we investigate the commutativity of addition of prime near-rings satisfying certain identities involving right ()-3-derivation

On Generalized (θ, θ) -3 -Derivations in Prime Near-Rings

Let N be a near-ring and is a mapping on N . In this paper we introduce the notion of generalized (θ, θ)-3-derivation in near-ring N . Also we investigate the commutativity of addition of near-rings satisfying certain identities involving generalized (θ,θ)-3-derivation on prime near-rings

Jordan (θ, θ)*- Derivation Pairs of Rings With Involution

Let  R be a 6-torsion  free ring with involution , θ  is a mapping of R and let (d,g) : R→R be an additive mapping . In this paper  we will give the relation between (θ, θ)*-derivation pair and Jordan (θ, θ)*-derivation pair . Also , we will prove that if (d,g) is a Jordan (θ, θ)*-derivation pair , then d is a Jordan (θ, θ)*-derivation

Jordan left (?,?) -derivations Of ?-prime rings

It was known that every left (?,?) -derivation is a Jordan left (?,?) – derivation on ?-prime rings but the converse need not be true. In this paper we give conditions to the converse to be true

Double Reverse Theta *- Centralizer of Rings With Involution

Let R be a ring with involution and θ is a mapping of R. It was known that every double reverse θ* - centralizer is a double Jordan θ* - centralizer on R but the converse need not be true . In this paper we give conditions to the converse to be true