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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.

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 ≠ 0 ) then there exists λ from the extended centroid of R such that T = λ S ( S = λ T ) .

An identity related to centralizers in semiprime rings

Joso Vukman — 1999

Commentationes Mathematicae Universitatis Carolinae

The purpose of this paper is to prove the following result: Let R be a 2 -torsion free semiprime ring and let T : R → R be an additive mapping, such that 2 T ( x 2 ) = T ( x ) x + x T ( x ) holds for all x ∈ R . In this case T is left and right centralizer.

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