Centralizers and Lie ideals
Centralizers on prime and semiprime rings
The purpose of this paper is to investigate identities satisfied by centralizers on prime and semiprime rings. We prove the following result: Let be a noncommutative prime ring of characteristic different from two and let and be left centralizers on . Suppose that is fulfilled for all . If
Centralizers on semiprime rings
The main result: Let be a -torsion free semiprime ring and let be an additive mapping. Suppose that holds for all . In this case is a centralizer.
Centralizing and commuting generalized derivations on prime rings
Characterisations of Semi-Prime Archimedean f-algebras.
Classical quotient rings of generalized matrix rings.
Cocentralizing and vanishing derivations on multilinear polynomials in prime rings.
Commutativity conditions on derivations and Lie ideals in -prime rings.
Commutativity of *-prime rings with generalized derivations
Commutativity results for semiprime rings with derivations.
Commutativity theorems for rings with differential identities on Jordan ideals
In this paper we investigate commutativity of ring with involution which admits a derivation satisfying certain algebraic identities on Jordan ideals of . Some related results for prime rings are also discussed. Finally, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.
Compatible ideals and radicals of Ore extensions.