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Semiprime FDI-rings

Gubareni N.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 4

49--59

In this paper we present some results for FDI-rings, i.e. rings with a complete set of pairwise orthogonal primitive idempotents. We consider the nilpotency index of ideals and give its upper band for ideals in some classes of rings. We also give a new proof of a criterion of semiprime FDI-rings to be prime.

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

Vukman J.

Demonstratio Mathematica

2008

Vol. 41, nr 4

773-778

An identity with derivations on rings and Banach algebras

Fosner A., Fosner M., Vukman J.

Demonstratio Mathematica

2008

Vol. 41, nr 3

525-530

Generalized Jordan derivations on semiprime rings

Wei F., Xiao Z.

Demonstratio Mathematica

2007

Vol. 40, nr 4

789-798

It is shown that, given a 2-torsion-free semiprime ring with unit e, every generalized Jordan derivation on R is a generalized derivation. Let n be a fixed positive integer, R be a noncommutative (n+1)!-torsion-free prime ring with the center CR. It is proved that, if [..]: R -> R is a generalized Jordan derivation of R such that [..](x)xn + x [...].