Multiplicative Lie Isomorphisms Between Prime Rings

Centralizing traces and Lie triple isomorphisms on generalized matrix algebras

“…for all a 2 ∈ A 2 , a 4 ∈ A 4 , where κ = ϕ(f 11 (1, 1)) − k 11 (1,1). Similarly, using (3.36) and (3.46) we have…”

“…The involved rings and operator algebras include (semi-)prime rings, the algebra of bounded linear operators, C * -algebras, von Neumann algebras, H * -algebras, Banach space nest algebras, Hilbert space nest algebras, reflexive algebras, see [1,2,3,26,27,28,29,57,59,60,61,62,65,66,69,70,71,76,78]. One recent remarkable work concerning Lie isomorphisms between Bnanach space nest algebras is due to Qi, Hou and Deng [68].…”

Lie derivable mappings on prime rings

“…We only show (1). Since a ij ∈ T ij , there exist a ij ∈ R ij and c ∈ C such that a ij = a ij c. Therefore, a ij x jk = 0 for all x jk ∈ R jk is equivalent to a ij cxe k = 0 for all x ∈ R. It follows that a ij xe k = 0 since C is a field.…”

“…These mappings include multiplicative maps, (Jordan) derivable mappings, Jordan (triple) mappings, Jordan elementary mappings, and so on (see [1], [4]- [8], and references therein). For example, in his pioneer paper [8], Martindale III obtained the following result.…”

Strong commutativity preserving generalized derivations on right ideals

“…research area in matrix theory, operator theory and ring theory (see for instance [2,6,9,[11][12][13]15,16,20,32,[41][42][43][44][45]47]). In [5] Bell and Daif investigated a certain kind of commutativity preserving maps as follows: Let S be a subset of R. A map f : S → R is called strong commutativity preserving (SCP) on S if [ f (x), f (y)] = [x, y] for all x, y ∈ S. Precisely, they proved that if a semiprime ring R admits a derivation which is SCP on a right ideal ρ, then ρ ⊆ Z (R).…”