[PDF] Top 20 Generalized derivations in prime rings

... a prime ring and I be a nonzero ideal of ...are generalized derivations, associated with derivations d, g, h : R → R respectively and α : R → R is any map such that F (xy) + G(x)H(y) + [α(x), ... See full document

... of prime rings with derivations was initiated by ...studied generalized derivations in prime ...left generalized derivation on prime ring is ...of prime ... See full document

... a prime ring of char (R) 6= 2, Z the center of R, and L a nonzero Lie ideal of ...a generalized derivation F associated with a derivation d which acts as a homomorphism or as anti-homomorphism on L, then ... See full document

... additive function F : R → R is called a generalized derivation if there exists a derivation d : R → R such that F(xy) = F(x)y + xd(y) holds for all x, y ∈ R. In this paper, we prove that d = 0 or U ⊆ Z(R) if any ... See full document

... a prime Γ -ring ܯ for which ܯ is commutative with the conditions ݀(ܷ) ⊆ ܷ and ݀ ଶ (ܷ) ⊆ ܼ , where ܷ is an ideal of ܯ and ܼ is the centre of ܯ ...completely prime Γ -ring which is a ...completely ... See full document

... of Generalized derivations in ...of Generalized derivations in semiprime gamma rings Bresar [2] studied on the distance of the composition of two derivations to the ... See full document

... on prime rings was obtained by Mayne ...that derivations, automorphisms, and some related maps cannot be centralizing on certain subsets of noncommutative prime (and some other) ...a ... See full document

... studied generalized derivations of prime ...noncommutative prime ring R, a is a fixed element of R and F is an generalized derivation on R associated with a derivation d then the ... See full document

... reverse derivations were presented. The reverse derivations on semi prime rings have been studied by Samman and Alyamani ...semi prime rings by using reverse ...the ... See full document

... a generalized derivation of R if there exists a derivation d from R to R such that gxy gxy xdy holds for all x, y ∈ ...a generalized derivation of R. Thus, generalized derivation covers both the ... See full document

... Throughout R will represent an associative ring with identity, Z(R) denoted to the center of R ,R is said to be n-torsion free, where n ≠ 0 is an integer, if whenever n x= 0,with x ∈ R, then x = 0. We recall that R is ... See full document

... been generalized in different directions by various authors ( for reference see [1, 3, ...have generalized the notion of multiplicative derivation by introducing the notion of generalized ... See full document

... course, derivations which are not endomorphisms or antiendomorphisms on 𝑅 may behave as such on certain subsets of 𝑅; for example, any derivation 𝑑 behaves as the zero endomorphism on the subring 𝐶 consisting of ... See full document

... left generalized ( , )-4-derivation in near-ring N and we determine some conditions of left generalized ( , )-4-derivation and semigroup ideals which make prime near-ring commutative ring ... See full document

... of derivations, generalized derivations, generalized multiplicative derivations( for reference see [1, 3, 4, 5, 6, 7, 8, 9], where further references can be ...left generalized ... See full document

... Theorem 3.3: Let 𝑁 be a 3-prime near ring and 𝑈 1 , 𝑈 2 , . . . , 𝑈 𝑛 be nonzero semigroup ideals of 𝑁 . Let 𝜎, 𝜏 be mappings on 𝑁 such that 𝜎(𝑈 𝑖 ) = 𝑈 𝑖 , 𝜏(𝑈 𝑖 ) = 𝑈 𝑖 for 𝑖 = 1,2, . . . , 𝑛 . If 𝐹 1 , 𝐹 2 are ... See full document

... using derivations was initiated by Bell and Mason in 1987 in ...from rings to near-rings with derivations in ...a generalized derivation if it is both a left and a right ... See full document

... called prime if aΓRΓb = 0 with a, b ∈R implies a = 0 or b = 0, and R is called semi prime if aΓRΓa = 0 with a ∈R implies a = ...semi-) prime Γ-ring is an extension for the notion of a ... See full document

... is prime and ...Jordan derivations d and g on A/P are also a pair of derivations on A/P by Breˇsar ...continuous derivations on commutative semisimple Banach ... See full document

... of generalized higher left centralizer, generalized Jordan higher left centralizer of R, as well as we prove that every Jordan higher torsion free prime ring R is higher left centralizer of ...every ... See full document