Notes on -derivations.
On a subset with nilpotent values in a prime ring with derivation
Let be a prime ring, with no non-zero nil right ideal, a non-zero drivation of , a non-zero two-sided ideal of . If, for any , , there exists such that , then is commutative. As a consequence we extend the result to Lie ideals.
On Anti-inverse Rings
On anti-inverse rings.
On center-like elements in rings.
On centralizers of semiprime rings
Let be a semiprime ring and an additive mapping such that holds for all . Then is a left centralizer of . It is also proved that Jordan centralizers and centralizers of coincide.
On commutativity of one-sided -unital rings.
On commutativity of P.I. rings.
On commutativity of P.I. rings. (Short Communication).
On commutativity of rings with constraints on subsets
On commutativity theorems for rings.
On dependent elements in rings.
On derivations and commutativity in prime rings.
On Galois projective group rings.
On generalized periodic-like rings.
On Jordan ideals and derivations in rings with involution
Let be a -torsion free -prime ring, a derivation which commutes with and a -Jordan ideal and a subring of . In this paper, it is shown that if either acts as a homomorphism or as an anti-homomorphism on , then or . Furthermore, an example is given to demonstrate that the -primeness hypothesis is not superfluous.
On Jordan ideals and left -derivations in prime rings.
On Lie ideals with generalized derivations.
On modules in which idempotent reducts form a chain
On near-ring ideals with -derivation
Let be a -prime left near-ring with multiplicative center , a -derivation on is defined to be an additive endomorphism satisfying the product rule for all , where and are automorphisms of . A nonempty subset of will be called a semigroup right ideal (resp. semigroup left ideal) if (resp. ) and if is both a semigroup right ideal and a semigroup left ideal, it be called a semigroup ideal. We prove the following results: Let be a