• Title/Summary/Keyword: (generalized) derivation

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SEMIPRIME NEAR-RINGS WITH ORTHOGONAL DERIVATIONS

  • Park, Kyoo-Hong;Jung, Yong-Soo
    • The Pure and Applied Mathematics
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    • v.13 no.4 s.34
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    • pp.303-310
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    • 2006
  • M. $Bre\v{s}ar$ and J. Vukman obtained some results concerning orthogonal derivations in semiprime rings which are related to the result that is well-known to a theorem of Posner for the product of two derivations in prime rings. In this paper, we present orthogonal generalized derivations in semiprime near-rings.

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APPROXIMATELY QUADRATIC DERIVATIONS AND GENERALIZED HOMOMORPHISMS

  • Park, Kyoo-Hong;Jung, Yong-Soo
    • The Pure and Applied Mathematics
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    • v.17 no.2
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    • pp.115-130
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    • 2010
  • Let $\cal{A}$ be a unital Banach algebra. If f : $\cal{A}{\rightarrow}\cal{A}$ is an approximately quadratic derivation in the sense of Hyers-Ulam-J.M. Rassias, then f : $\cal{A}{\rightarrow}\cal{A}$ is anexactly quadratic derivation. On the other hands, let $\cal{A}$ and $\cal{B}$ be Banach algebras.Any approximately generalized homomorphism f : $\cal{A}{\rightarrow}\cal{B}$ corresponding to Cauchy, Jensen functional equation can be estimated by a generalized homomorphism.

τ-CENTRALIZERS AND GENERALIZED DERIVATIONS

  • Zhou, Jiren
    • Journal of the Korean Mathematical Society
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    • v.47 no.3
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    • pp.523-535
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    • 2010
  • In this paper, we show that Jordan $\tau$-centralizers and local $\tau$-centralizers are $\tau$-centralizers under certain conditions. We also discuss a new type of generalized derivations associated with Hochschild 2-cocycles and introduce a special local generalized derivation associated with Hochschild 2-cocycles. We prove that if $\cal{L}$ is a CDCSL and $\cal{M}$ is a dual normal unital Banach $alg\cal{L}$-bimodule, then every local generalized derivation of above type from $alg\cal{L}$ into $\cal{M}$ is a generalized derivation.

ON LIE IDEALS OF PRIME RINGS WITH GENERALIZED JORDAN DERIVATION

  • Golbasi, Oznur;Aydin, Neset
    • East Asian mathematical journal
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    • v.21 no.1
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    • pp.21-26
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    • 2005
  • The purpose of this paper is to show that every generalized Jordan derivation of prime ring with characteristic not two is a generalized derivation on a nonzero Lie ideal U of R such that $u^2{\in}U\;for\;{\forall}u{\in}U$ which is a generalization of the well-known result of I. N. Herstein.

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ON GENERALIZED SYMMETRIC BI-DERIVATIONS IN PRIME RINGS

  • Ozturk, M. Ali;Sapanci, Mehmet
    • East Asian mathematical journal
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    • v.15 no.2
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    • pp.165-176
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    • 1999
  • After the derivation was defined in [19] by Posner a lot of researchers studied the derivations in ring theory in different manners such as in [2], [4], [5], ..., etc. Furthermore, many researches followed the definition of the generalized derivation([3], [6], [7], ..., etc.). Finally, Maksa defined a symmetric bi-derivation and many researches have been done in ring theory by using this definition. In this work, defining a symmetric bi-$\alpha$-derivation, we study the mentioned researches above in the light of this new concept.

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ON GENERALIZED (α, β)-DERIVATIONS IN BCI-ALGEBRAS

  • Al-Roqi, Abdullah M.
    • Journal of applied mathematics & informatics
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    • v.32 no.1_2
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    • pp.27-38
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    • 2014
  • The notion of generalized (regular) (${\alpha},\;{\beta}$)-derivations of a BCI-algebra is introduced, some useful examples are discussed, and related properties are investigated. The condition for a generalized (${\alpha},\;{\beta}$)-derivation to be regular is provided. The concepts of a generalized F-invariant (${\alpha},\;{\beta}$)-derivation and ${\alpha}$-ideal are introduced, and their relations are discussed. Moreover, some results on regular generalized (${\alpha},\;{\beta}$)-derivations are proved.