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A note on normability of locally convex spaces

Joso Vukman — 1983

Commentationes Mathematicae Universitatis Carolinae

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 $x \in R$ . 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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Currently displaying 1 – 8 of 8

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

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.