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Generalized Skew Derivations Implemented by Elementary Operators

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Abstract

Let R be a semiprime ring with the maximal right ring of quotients Q mr . An additive map d: R →Q mr is called a generalized skew derivation if there exists a ring endomorphism σ:R →R and a map \(\d:R \to Q_{mr}\) such that \(d(xy)=\d(x)y+\sigma(x)d(y)\) for all x,y ∈ R. If σ is surjective, we determine the structure of generalized skew derivations for which there exists a finite number of elements a i ,b i  ∈ Q mr such that d(x) = a 1 xb 1 + ⋯ + a n xb n for all x ∈ R.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, FNM, University of Maribor, 2000, Maribor, Slovenia

    Daniel Eremita

  2. Department of Mathematics, University of Zagreb, Bijenička 30, 10000, Zagreb, Croatia

    Ilja Gogić & Dijana Ilišević

  3. Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000, Novi Sad, Serbia

    Ilja Gogić

Authors
  1. Daniel Eremita
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  2. Ilja Gogić
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  3. Dijana Ilišević
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Corresponding author

Correspondence to Ilja Gogić.

Additional information

The third author was supported by the Ministry of Science, Educations and Sports of the Republic of Croatia (Grant 037-0372784-2757).

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Eremita, D., Gogić, I. & Ilišević, D. Generalized Skew Derivations Implemented by Elementary Operators. Algebr Represent Theor 17, 983–996 (2014). https://doi.org/10.1007/s10468-013-9429-8

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  • DOI: https://doi.org/10.1007/s10468-013-9429-8

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