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1
Content available remote The strict topology on topological algebras
EN
In this paper, we define strict, uniform and compact-open topologies on a topological algebra and investigate their properties. These results unify and include several results of other authors.
2
Content available remote On (α, β)-derivations of semiprime rings, II
3
Content available remote Centralizing mappings and derivations on semiprime rings
EN
In this paper we study some properties of centralizing mappings on semi-prime rings. The main purpose is to prove the result: Let -R be a semiprime ring and f an endomorphism of R, g an epimorphism of R such that the mapping x -> [f(x),g(x)] is central. Then [f(x),g(x)] = 0 holds for all x e R. We also establish some results about (alpha,beta)-derivations.
4
Content available remote A note on (alpha)-derivations on semiprime rings
EN
In this note we investigate some properties of a-derivations on prime and semiprime rings. We establish some identities for a commuting a-derivation d on a semiprime ring R and show that d maps R into its center and obtain some well-known results as a consequence. We also generalize Posner's theorem on the composition of derivations for a-derivations and as an application resolve a functional equation of automorphisms on certain prime rings.
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