Displaying similar documents to “Symmetric bi-derivations on prime and semi-prime rings.”

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.

A Unified approach to the Structure Theory of PI-Rings and GPI-Rings

Brešar, Matej (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 16R20, 16R50, 16R60, 16N60. We give short proofs, based only on basic properties of the extended centroid of a prime ring, of Martindale’s theorem on prime GPI-rings and (a strengthened version of) Posner’s theorem on prime PI-rings. * Supported by the Slovenian Research Agency (program No. P1-0288).

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.