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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....

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

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

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Periodic rings with finitely generated underlying group.

Khazal, R., Dăscălescu, S. (2004)

International Journal of Mathematics and Mathematical Sciences

Prime and semiprime rings with symmetric skew n-derivations

Ajda Fošner (2014)

Colloquium Mathematicae

Let n ≥ 3 be a positive integer. We study symmetric skew n-derivations of prime and semiprime rings and prove that under some certain conditions a prime ring with a nonzero symmetric skew n-derivation has to be commutative.

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On rings with prime centers.

On some commutativity theorems for finite rings and finite groups

On structure of certain periodic rings and near-rings.

On the commutator ideal of certain rings

On the generalized hypercentralizer of a Lie ideal in a prime ring

On the mapping $x y \to {(x y)}^{n}$ in an associative ring.

On weakly reversible rings.

On weakly $π$ -subcommutative near-rings.

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

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

Periodic rings with finitely generated underlying group.

Prime and semiprime rings with symmetric skew n-derivations

Prime rings with hypercommuting derivations on a Lie ideal

Remarks on derivations on semiprime rings.

Remarks on generalized derivations in prime and semiprime rings.

Rings with Dense Quasi-Centre.

Some commutativity results for rings

Some results for generalized Lie ideals in prime rings with derivation. II.

Some small-centralizer properties for rings.

Strong commutativity preserving maps on Lie ideals of semiprime rings.

Currently displaying 61 – 80 of 98