[PDF] Top 20 Multiplicative (Generalized) Reverse Derivations on Semiprime Ring

... a semiprime ring and F be a non-zero multiplicative (generalized) reverse derivation associated with a map d, I be a non-zero ideal of ... See full document

... the generalized derivation F ...same generalized polynomial identities with coefficients in U ...prime ring and d a nonzero derivation on R and I be a nonzero ideal of ... See full document

... a ring a concept more general than a ring was definedby Nobusawa ...near ring has been introduced by Bell and ...of derivations in near ...and semiprime rings admitting suitably ... See full document

... a semiprime near-ring if xN x = {0} implies x = ...the multiplicative center of N , that is, Z = {x ∈ N | xy = yx for all y ∈ N ...the multiplicative commutator of x and y, while the symbol ... See full document

... and generalized by Barnes 1966 (1) as above ...every ring is Г-ring ...be semiprime if xГMГx=0 implies that x=0 for all x,y 𝜖M ,(2) ...Г- ring as follows :An additive mapping d:M→M is ... See full document

... left generalized derivation with associated derivation d if F(xy) = d(x)y + xF (y), for all x, y ∈ N ...a generalized derivation with associated derivation d if it is both a left as well as a right ... See full document

... also derivations on rings can tell us about the structure of the ...a ring is commutative if and only if the only inner derivation on the ring is ...Also derivations can be helpful for ... See full document

... orthogonal generalized derivations of semiprime associative ...[1] generalized some results of [2] for a nonzero ideal of a semiprime associative ...of derivations and ... See full document

... with multiplicative centre ZN. Recall that a Γ-near-ring N is prime if xΓNΓy 0 implies x 0 or y ...a generalized derivation if there exits a derivation d of N such that fxαy f xαy xαdy for all x, y ∈ ... See full document

... prime ring of characteristic di ff erent from 2 is either an isomorphism or an ...are semiprime rings does not ...prime ring of characteristic dif- ferent from 2 is a derivation ... See full document

... prime ring of characteristic not two admitting a nonzero derivation d such that [d(x), d(y)] = 0 for all x, y ∈ R, then R is ...free semiprime ring R admits a nonzero deriva- tion d such that [d(x), ... See full document

... in ring theory ...of ring theory. Hvala [4] introduced the concept of Generalized derivations in ...of Generalized derivations in semiprime gamma rings Bresar [2] studied ... See full document

... garding generalized inner derivations, we consider a general situation regarding a pair of derivations of a semiprime ring and prove the ...a semiprime ring R satisfying f ... See full document

... with derivations and automorphisms on semiprime ...2-torsion-free semiprime ring, such that [D(x)x + xα(x),x] = 0 holds for all x ∈ R, then D and α − I , where I denotes the identity mapping, ... See full document

... Jordan derivations and Jordan left derivations of 2 and 3-torsion free semiprime Γ ...worked derivations and generalized derivations on Lie ideals of completely semiprime ... See full document

... a semiprime near- ring if xN x = {0} implies x = ...the multiplicative center of N , that is, Z = {x ∈ N | xy = yx for all y ∈ N ...the multiplicative commutator of x and y, while the symbol ... See full document

... that derivations, automorphisms, and some related maps cannot be centralizing on certain subsets of noncommutative prime (and some other) ...prime ring R of characteristic not 2 was given and subsequently ... See full document

... prime ring, U the Utumi quotient ring of R, C = Z(U ) the extended centroid of R, L a non-central Lie ideal of R, H and G non-zero generalized derivations of ... See full document

... Proof. Let d be the associated derivation of F. By Theorem 2.4, we conclude that either dI 0 or R is commutative. Assume that R is not commutative. Then dI 0. Since R is a prime ring, dI 0 implies dR 0 and hence ... See full document

... studied generalized derivations of prime ...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 condition Fx, a 0 or Fx, a 0 ... See full document