Derivations and automorphisms of $L\sp{1}\,(0,\,1)$

Derivations and Automorphisms of Certain Operator Algebras

A Note on Automorphisms and Derivations of Lie Algebras

In a recent paper Borel and Serre proved the theorem: If 8 is a Lie algebra of characteristic 0 and 8 has an automorphism of prime period without fixed points f^O, then 8 is nilpotent.1 In this note we give a proof valid also for characteristic p^O. By the same method we can prove several other similar results on automorphisms and derivations. Our method is based on decompositions of the Lie al...

Centralizing automorphisms and Jordan left derivations on σ-prime rings

Let R be a 2-torsion free σ-prime ring. It is shown here that if U 6⊂ Z(R) is a σ-Lie ideal of R and a, b in R such that aUb = σ(a)Ub = 0, then either a = 0 or b = 0. This result is then applied to study the relationship between the structure of R and certain automorphisms on R. To end this paper, we describe additive maps d : R −→ R such that d(u) = 2ud(u) where u ∈ U, a nonzero σ-square close...

Linear codes using skew polynomials with automorphisms and derivations

In this work the definition of codes as modules over skew polynomial rings of automorphism type is generalized to skew polynomial rings, whose multiplication is defined using an automorphism and a derivation. This produces a more general class of codes which, in some cases, produce better distance bounds than module skew codes constructed only with an automorphism. Extending the approach of Gab...

Identities with derivations and automorphisms on semiprime rings

The purpose of this paper is to investigate identities with derivations and automorphisms on semiprime rings. A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. Mayne proved that in case there exists a nontrivial centralizing automorphism on a prime ring, then the ring is commutative. In this paper, some...