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Let $R$ be a 2-torsion free prime ring and let $σ, τ$ be automorphisms of $R$ . For any $x, y \in R$ , set ${[x, y]}_{σ, τ} = x σ (y) - τ (y) x$ . Suppose that $d$ is a $(σ, τ)$ -derivation defined on $R$ . In the present paper it is shown that $(i)$ if $R$ satisfies ${[d (x), x]}_{σ, τ} = 0$ , then either $d = 0$ or $R$ is commutative $(i i)$ if $I$ is a nonzero ideal of $R$ such that $[d (x), d (y)] = 0$ , for all $x, y \in I$ , and $d$ commutes with both $σ$ and $τ$ , then either $d = 0$ or $R$ is commutative. $(i i i)$ if $I$ is a nonzero ideal of $R$ such that $d (x y) = d (y x)$ , for all $x, y \in I$ , and $d$ commutes with $τ$ , then $R$ is commutative. Finally a related result has been obtain for $(σ, τ)$ -derivation....

On $τ$ -centralizers of semiprime rings.

Albaş, Emine (2007)

Sibirskij Matematicheskij Zhurnal

Order completions of semiprime rings

Walter D. Burgess, Robert M. Raphael (1981)

Czechoslovak Mathematical Journal

Ordinary selfdistributive rings

Sobhy Ghoneim, Marian Kechlibar, Tomáš Kepka (2005)

Commentationes Mathematicae Universitatis Carolinae

Left selfdistributive rings (i.e., $x y z = x y x z$ ) which are semidirect sums of boolean rings and rings nilpotent of index at most 3 are studied.

Ore extensions over near pseudo-valuation rings.

Bhat, V.K. (2009)

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

Orthogonal generalized $(σ, τ)$ -derivations of semiprime rings.

Gölbaşi, Öznur, Aydin, Neşet (2007)

Sibirskij Matematicheskij Zhurnal

$P (r, m)$ near-rings.

Balakrishnan, R., Suryanarayanan, S. (2000)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Polynomial identities and radicals

B. J. Gardner (1977)

Compositio Mathematica

Polynomial identities of nil algebras of bounded index

Francesca Benanti, Vesselin Drensky (1999)

Bollettino dell'Unione Matematica Italiana

Lo scopo di questo lavoro è di dare una nuova descrizione del $T$ -ideale generato dalla nil-identità $x^{n} = 0$ come immagine omeomorfa della $n$ -esima potenza tensoriale simmetrica dell'algebra associativa libera $K 〈X〉$ su un campo $K$ di caratteristica $0$ . Come applicazione calcoliamo il carattere delle conseguenze multilineari di grado $\leq n + 2$ dell'identità $x^{n} = 0$ .

Posner's second theorem and an annihilator condition.

De Filippis, V., Di Vincenzo, O.M. (2001)

Mathematica Pannonica

Posner's second theorem and annihilator conditions with generalized skew derivations

Vincenzo De Filippis, Feng Wei (2012)

Colloquium Mathematicae

Let be a prime ring of characteristic different from 2, $_{r}$ be its right Martindale quotient ring and be its extended centroid. Suppose that is a non-zero generalized skew derivation of and f(x₁,..., xₙ) is a non-central multilinear polynomial over with n non-commuting variables. If there exists a non-zero element a of such that a[ (f(r₁,..., rₙ)),f(r₁, ..., rₙ)] = 0 for all r₁, ..., rₙ ∈ , then one of the following holds: (a) there exists λ ∈ such that (x) = λx for all x ∈ ; (b) there exist $q \in_{r}$ and...

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Displaying 241 – 260 of 510

On uniformly strongly prime Γ-semirings (II)

On unital extensions of near-rings and their radicals.

On von Neumann regular rings. VII.

On waists of right distributive rings.

On zero subrings and periodic subrings.

On $(σ, τ)$ -derivations in prime rings