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Sibirsk. Mat. Zh., 2015, Volume 56, Number 2, Pages 241–248 (Mi smj2635)  

This article is cited in 3 scientific papers (total in 3 papers)

Generalized reverse derivations on semiprime rings

A. Aboubakrab, S. Gonzáleza

a Universidad de Oviedo, Oviedo 33007 Spain
b University of Fayoum, Fayoum 63514 Egypt

Abstract: We generalize the notion of reverse derivation by introducing generalized reverse derivations. We define an $l$-generalized reverse derivation ($r$-generalized reverse derivation) as an additive mapping $F\colon R\to R$, satisfying $F(xy)=F(y)x+yd(x)$ ($F(xy)=d(y)x+yF(x)$) for all $x,y\in R$, where $d$ is a reverse derivation of $R$. We study the relationship between generalized reverse derivations and generalized derivations on an ideal in a semiprime ring. We prove that if $F$ is an $l$-generalized reverse (or $r$-generalized) derivation on a semiprime ring $R$, then $R$ has a nonzero central ideal.

Keywords: semiprime ring, ideal, derivation, reverse derivation, $l$-generalized derivation, $r$-generalized derivation, l-generalized reverse derivation, r-generalized reverse derivation.

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English version:
Siberian Mathematical Journal, 2015, 56:2, 199–205

Bibliographic databases:

UDC: 512.552.34
Received: 04.02.2014

Citation: A. Aboubakr, S. González, “Generalized reverse derivations on semiprime rings”, Sibirsk. Mat. Zh., 56:2 (2015), 241–248; Siberian Math. J., 56:2 (2015), 199–205

Citation in format AMSBIB
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\paper Generalized reverse derivations on semiprime rings
\jour Sibirsk. Mat. Zh.
\yr 2015
\vol 56
\issue 2
\pages 241--248
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\transl
\jour Siberian Math. J.
\yr 2015
\vol 56
\issue 2
\pages 199--205
\crossref{https://doi.org/10.1134/S0037446615020019}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. H. Nabiel, “Derivations, generalized derivations, and -derivations of period 2 in rings”, Turk. J. Math., 42:5 (2018), 2664–2671  crossref  mathscinet  zmath  isi  scopus
    2. A. Ali, A. Bano, “Multiplicative (generalized) reverse derivations on semiprime ring”, Eur. J. Pure Appl Math., 11:3 (2018), 717–729  crossref  mathscinet  zmath  isi
    3. S. K. Tiwari, R. K. Sharma, B. Dhara, “Some theorems of commutativity on semiprime rings with mappings”, Southeast Asian Bull. Math., 42:2 (2018), 279–292  mathscinet  zmath  isi
  • Сибирский математический журнал Siberian Mathematical Journal
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