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On (m, n)-Jordan derivations and commutativity of prime rings

Vukman J.

Demonstratio Mathematica

2008

Vol. 41, nr 4

773-778

On left multipliers and the commutativity of prime rings

Ashraf M., Ali S.

Demonstratio Mathematica

2008

Vol. 41, nr 4

763-771

Let R be an associative ring. An additive mapping H : R —> R is called a left multiplier if H(xy) = H(x)y, holds for all x, y e R. In this paper, we investigate commutativity of prime rings satisfying certain identities involving left multiplier. Some related results have also been discussed.

An identity with derivations on rings and Banach algebras

Fosner A., Fosner M., Vukman J.

Demonstratio Mathematica

2008

Vol. 41, nr 3

525-530

Context-Free and E0L Derivations over Free Groups

Meduna A., Bildo R., Blatny' P.

Schedae Informaticae

2007

Vol. 16

9-20

In the context-free and E0L grammars discussed in this pa- per, the derivations are introduced over free groups rather than free monoids. It is proved that both grammars with derivations introduced in this way characterize the family of recursively enumerable languages in a very succinct way. Specifically, this characterization is based on the eight-nonterminal context-free grammars and six-nonterminal E0L grammars over free groups.

On semiderivations of prime rings

Ashrat M., Rehman N.

Demonstratio Mathematica

2004

Vol. 37, nr 2

275--284

On Jordan ideals and Jordan derivations of prime rings

Ashrat M., Rehman N.

Demonstratio Mathematica

2004

Vol. 37, nr 3

517--523

Let R be a 2-torsion free prime ring, and let J be a nonzero Jordan ideal and a subring of R. In the present paper it is shown that if d is an additive mapping of R into itself satisfying d(u2) = d(u)u + ud(u), for all u 6 J, then d(uv) = d(u)v + ud(v), for all u, v J.

Centralizing mappings and derivations on semiprime rings

Chaudhry M., Thaheem A.

Demonstratio Mathematica

2004

Vol. 37, nr 2

285--292

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.