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On a subset with nilpotent values in a prime ring with derivation

Vincenzo De Filippis (2002)

Bollettino dell'Unione Matematica Italiana

Let $R$ be a prime ring, with no non-zero nil right ideal, $d$ a non-zero drivation of $R$ , $I$ a non-zero two-sided ideal of $R$ . If, for any $x$ , $y \in I$ , there exists $n = n (x, y) \geq 1$ such that ${(d ([x, y]) - [x, y])}^{n} = 0$ , then $R$ is commutative. As a consequence we extend the result to Lie ideals.

On Anti-inverse Rings

Hisao Tominaga (1983)

Publications de l'Institut Mathématique

On anti-inverse rings.

Tominaga, Hisao (1983)

Publications de l'Institut Mathématique. Nouvelle Série

On center-like elements in rings.

Fisher, Joe W., Fahmy, Mohamed H. (1985)

International Journal of Mathematics and Mathematical Sciences

On centralizers of semiprime rings

Borut Zalar (1991)

Commentationes Mathematicae Universitatis Carolinae

Let $𝒦$ be a semiprime ring and $T : 𝒦 \to 𝒦$ an additive mapping such that $T (x^{2}) = T (x) x$ holds for all $x \in 𝒦$ . Then $T$ is a left centralizer of $𝒦$ . It is also proved that Jordan centralizers and centralizers of $𝒦$ coincide.

On commutativity of one-sided $s$ -unital rings.

Abujabal, H.A.S., Khan, M.A. (1992)

International Journal of Mathematics and Mathematical Sciences

On commutativity of P.I. rings.

Howard E. Bell (1983)

Aequationes mathematicae

On commutativity of P.I. rings. (Short Communication).

Howard E. Bell (1983)

Aequationes mathematicae

On commutativity of rings with constraints on subsets

H. A. S. Abujabal, M. A. Khan, M. S. Khan, Mohammad S. Samman (1993)

Czechoslovak Mathematical Journal

On commutativity theorems for rings.

Abujabal, H.A.S., Khan, M.S. (1990)

International Journal of Mathematics and Mathematical Sciences

On dependent elements in rings.

Vukman, Joso, Kosi-Ulbl, Irena (2004)

International Journal of Mathematics and Mathematical Sciences

On derivations and commutativity in prime rings.

De Filippis, Vincenzo (2004)

International Journal of Mathematics and Mathematical Sciences

On Galois projective group rings.

Szeto, George, Ma, Linjun (1991)

International Journal of Mathematics and Mathematical Sciences

On generalized periodic-like rings.

Bell, Howard E., Yaqub, Adil (2007)

International Journal of Mathematics and Mathematical Sciences

On Jordan ideals and derivations in rings with involution

Lahcen Oukhtite (2010)

Commentationes Mathematicae Universitatis Carolinae

Let $R$ be a $2$ -torsion free $*$ -prime ring, $d$ a derivation which commutes with $*$ and $J$ a $*$ -Jordan ideal and a subring of $R$ . In this paper, it is shown that if either $d$ acts as a homomorphism or as an anti-homomorphism on $J$ , then $d = 0$ or $J \subseteq Z (R)$ . Furthermore, an example is given to demonstrate that the $*$ -primeness hypothesis is not superfluous.

On Jordan ideals and left $(θ, θ)$ -derivations in prime rings.

Zaidi, S.M.A., Ashraf, Mohammad, Ali, Shakir (2004)

International Journal of Mathematics and Mathematical Sciences

On Lie ideals with generalized derivations.

Gölbaşı, Öznur, Kaya, Kazım (2006)

Sibirskij Matematicheskij Zhurnal

On modules in which idempotent reducts form a chain

Ágnes Szendrei (1978)

Colloquium Mathematicae

On near-ring ideals with $(σ, τ)$ -derivation

Öznur Golbaşi, Neşet Aydin (2007)

Archivum Mathematicum

Let $N$ be a $3$ -prime left near-ring with multiplicative center $Z$ , a $(σ, τ)$ -derivation $D$ on $N$ is defined to be an additive endomorphism satisfying the product rule $D (x y) = τ (x) D (y) + D (x) σ (y)$ for all $x, y \in N$ , where $σ$ and $τ$ are automorphisms of $N$ . A nonempty subset $U$ of $N$ will be called a semigroup right ideal (resp. semigroup left ideal) if $U N \subset U$ (resp. $N U \subset U$ ) and if $U$ is both a semigroup right ideal and a semigroup left ideal, it be called a semigroup ideal. We prove the following results: Let $D$ be a $(σ,$

On nearrings with derivation.

Khan, M.A., Khan, M.S. (2006)

Mathematica Pannonica

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