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2005•International Journal of Mathematics and Mathematical SciencesOpen access

On some equations related to derivations in rings

Joso Vukman, Irena Kosi-Ulbl

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Abstract

Let m and n be positive integers with m + n ≠ 0, and let R be an (m + n + 2)!‐torsion free semiprime ring with identity element. Suppose there exists an additive mapping D : R → R, such that D(xm+n+1) = (m + n + 1)xmD(x)xn is fulfilled for all x ∈ R, then D is a derivation which maps R into its center.

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Let m and n be positive integers with m + n ≠ 0, and let R be an (m + n + 2)!‐torsion free semiprime ring with identity element. Suppose there exists an additive mapping D : R → R, such that D(xm+n+1) = (m + n + 1)xmD(x)xn is fulfilled for all x ∈ R, then D is a derivation which maps R into its center.

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Available abstract

Let m and n be positive integers with m + n ≠ 0, and let R be an (m + n + 2)!‐torsion free semiprime ring with identity element. Suppose there exists an additive mapping D : R → R, such that D(xm+n+1) = (m + n + 1)xmD(x)xn is fulfilled for all x ∈ R, then D is a derivation which maps R into its center.

Key concepts: Algorithm, Computer science

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