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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 $S \neq 0$ $(T ...$

Centralizing and commuting generalized derivations on prime rings

Asif Ali, Tariq Shah (2008) Matematički Vesnik

Characterizations of Jordan derivations on triangular rings: additive maps Jordan derivable at idempotents.

An, Runling, Hou, Jinchuan (2010) ELA. The Electronic Journal of Linear Algebra [electronic only]

Cocentralizing and vanishing derivations on multilinear polynomials in prime rings.

De Filippis, Vincenzo (2009) Sibirskij Matematicheskij Zhurnal

Commutativity conditions on derivations and Lie ideals in $σ$ -prime rings.

Oukhtite, L., Salhi, S., Taoufiq, L. (2010)

Beiträge zur Algebra und Geometrie

Commutativity of prime $Γ$ -near rings with $Γ$ - $(σ, τ)$ -derivation.

Raina, Ravi, Bhat, V.K., Kumari, Neetu (2009)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

Commutativity results for semiprime rings with derivations.

Daif, Mohamad Nagy (1998)

International Journal of Mathematics and Mathematical Sciences

Commutativity theorems for rings with differential identities on Jordan ideals

L. Oukhtite, A. Mamouni, Mohammad Ashraf (2013)

Commentationes Mathematicae Universitatis Carolinae

In this paper we investigate commutativity of ring $R$ with involution $^{'} *^{'}$ which admits a derivation satisfying certain algebraic identities on Jordan ideals of $R$ . Some related results for prime rings are also discussed. Finally, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.

Compatible ideals and radicals of Ore extensions.

Hashemi, E. (2006)

The New York Journal of Mathematics [electronic only]

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