EUDML

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 $x \in R$ . If $S \neq 0$ $(T \neq 0)$ 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 $T : R \to R$ be an additive mapping, such that $2 T (x^{2}) = T (x) x + x T (x)$ holds for all $x \in R$ . In this case $T$ is left and right centralizer.

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 $T : R \to R$ be an additive mapping. Suppose that $T (x y x) = x T (y) x$ holds for all $x, y \in R$ . In this case $T$ is a centralizer.

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Identities with derivations and automorphisms on semiprime rings.

A note on derivations in semiprime rings.

On some equations related to derivations in rings.

On dependent elements in rings.

A note on normability of locally convex spaces

Centralizers on prime and semiprime rings

An identity related to centralizers in semiprime rings

Centralizers on semiprime rings