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Automorphisms and generalized skew derivations which are strong commutativity preserving on polynomials in prime and semiprime rings

Vincenzo de Filippis (2016)

Czechoslovak Mathematical Journal

Let R be a prime ring of characteristic different from 2, Q r its right Martindale quotient ring and C its extended centroid. Suppose that F , G are generalized skew derivations of R with the same associated automorphism α , and p ( x 1 , ... , x n ) is a non-central polynomial over C such that [ F ( x ) , α ( y ) ] = G ( [ x , y ] ) for all x , y ∈ { p ( r 1 , ... , r n ) : r 1 , ... , r n ∈ R } . Then there exists λ ∈ C such that F ( x ) = G ( x ) = λ α ( x ) for all x ∈ R .

Centralizers on prime and semiprime rings

Joso Vukman (1997)

Commentationes Mathematicae Universitatis Carolinae

The purpose of this paper is to investigate identities satisfied by centralizers on prime and semiprime rings. We prove the following result: Let R be a noncommutative prime ring of characteristic different from two and let S and T be left centralizers on R . Suppose that [ S ( x ) , T ( x ) ] S ( x ) + S ( x ) [ S ( x ) , T ( x ) ] = 0 is fulfilled for all x ∈ R . If S ≠ 0 ( T ...

Centralizers on semiprime rings

Joso Vukman (2001)

Commentationes Mathematicae Universitatis Carolinae

The main result: Let R be a 2 -torsion free semiprime ring and let T : R → R be an additive mapping. Suppose that T ( x y x ) = x T ( y ) x holds for all x , y ∈ R . In this case T is a centralizer.

Closure rings

Barry J. Gardner, Tim Stokes (1999)

Commentationes Mathematicae Universitatis Carolinae

We consider rings equipped with a closure operation defined in terms of a collection of commuting idempotents, generalising the idea of a topological closure operation defined on a ring of sets. We establish the basic properties of such rings, consider examples and construction methods, and then concentrate on rings which have a closure operation defined in terms of their lattice of central idempotents.

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