Semiprime Gamma Rings With Orthogonal Reverse Derivations

Ideal of Prime -Rings with Right Reverse Derivations

“…Recall that a -ring M is called prime if aMb = 0 implies a=0 or b=0and it is called semiprime if aMa = 0 implies a=0 ,a -ring M is called commutative if [ , ]  = 0 for all x,yM and ,Bresar and Vakman [2] have introduced the notion of a reverse derivation, the reverse derivation on semi prime rings have been studied by Samman and Alyamani [6] and K.KDey, A.IC.Paul, I.S.Rakhimov [3] have introduced the concepts of reverse derivation on -ring as an additive mapping d from M in to M is called reverse derivation if d(xy) = d(y)x + yd(x), for all x,yM ,and we consider an assumption (*) by xyz = xyz for all x,y,zU,,, where U is ideal of -ring.…”

On Commutativity of Prime and Semiprime - Rings with Reverse Derivations

“…Let M be Γ-ring, M is called a Γprime gamma ring if aΓM Γb = 0 with a, b ∊ M implies a = 0 or b = 0 [4], and M is called a Γsemiprime gamma ring if aΓM Γa = 0 with a ∊ M implies a = 0 [4]. [6]. In 2000, Kandamar [7] firstly introduced the notion of a k-derivation for a gamma ring in the sense of Barnes a.…”