• Title/Summary/Keyword: higher derivation

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JORDAN HIGHER DERIVATIONS ON TRIVIAL EXTENSION ALGEBRAS

  • Vishki, Hamid Reza Ebrahimi;Mirzavaziri, Madjid;Moafian, Fahimeh
    • Communications of the Korean Mathematical Society
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    • v.31 no.2
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    • pp.247-259
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    • 2016
  • We first give the constructions of (Jordan) higher derivations on a trivial extension algebra and then we provide some sufficient conditions under which a Jordan higher derivation on a trivial extension algebra is a higher derivation. We then proceed to the trivial generalized matrix algebras as a special trivial extension algebra. As an application we characterize the construction of Jordan higher derivations on a triangular algebra. We also provide some illuminating examples of Jordan higher derivations on certain trivial extension algebras which are not higher derivations.

HIGHER LEFT DERIVATIONS ON SEMIPRIME RINGS

  • Park, Kyoo-Hong
    • The Pure and Applied Mathematics
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    • v.17 no.4
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    • pp.355-362
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    • 2010
  • In this note, we extend the Bresar and Vukman's result [1, Proposition 1.6], which is well-known, to higher left derivations as follows: let R be a ring. (i) Under a certain condition, the existence of a nonzero higher left derivation implies that R is commutative. (ii) if R is semiprime, every higher left derivation on R is a higher derivation which maps R into its center.