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Displaying similar documents to “Vanishing power values of commutators with derivations.”

Prime and semiprime rings with symmetric skew n-derivations

Ajda Fošner (2014)

Colloquium Mathematicae

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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.

Lie ideals in prime Γ-rings with derivations

Nishteman N. Suliman, Abdul-Rahman H. Majeed (2013)

Discussiones Mathematicae - General Algebra and Applications

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Let M be a 2 and 3-torsion free prime Γ-ring, d a nonzero derivation on M and U a nonzero Lie ideal of M. In this paper it is proved that U is a central Lie ideal of M if d satisfies one of the following (i) d(U)⊂ Z, (ii) d(U)⊂ U and d²(U)=0, (iii) d(U)⊂ U, d²(U)⊂ Z.

Some results of reverse derivation on prime and semiprime Γ-rings

Neshtiman Nooraldeen Suliman (2015)

Discussiones Mathematicae - General Algebra and Applications

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In the present paper, it is introduced the definition of a reverse derivation on a Γ-ring M. It is shown that a mapping derivation on a semiprime Γ-ring M is central if and only if it is reverse derivation. Also it is shown that M is commutative if for all a,b ∈ I (I is an ideal of M) satisfying d(a) ∈ Z(M), and d(a ∘ b) = 0.

A note on rings of constants of derivations in integral domains

Piotr Jędrzejewicz (2011)

Colloquium Mathematicae

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We observe that the characterization of rings of constants of derivations in characteristic zero as algebraically closed subrings also holds in positive characteristic after some natural adaptation. We also present a characterization of such rings in terms of maximality in some families of rings.

Reduced near-rings

Szeto, George, Wong, Yuen-Fat (1981)

Portugaliae mathematica

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