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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


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1572-9176
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Identities related to generalized derivations in prime ∗-rings

Abdelkarim Boua
  • Department of Mathematics, Physics and Computer Science, Polydisciplinary Faculty, Sidi Mohammed Ben Abdellah University of Fez, LSI, Taza, Morocco
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/ Mohammed Ashraf
Published Online: 2019-10-15 | DOI: https://doi.org/10.1515/gmj-2019-2056

Abstract

Let be a prime ring with center Z() and * an involution of . Suppose that admits generalized derivations F, G and H associated with a nonzero derivation f, g and h of , respectively. In the present paper, we investigate the commutativity of a prime ring satisfying any of the following identities: (i) [F(x),F(x*)]=0, (ii) [F(x),F(x*)]=±[x,x*], (iii) F(x)F(x*)=0, (iv) F(x)F(x*)=±(xx*), (v) [F(x),x*]±[x,G(x*)]=0, (vi) F(xx*)Z(), (vii) F(x)G(x*)±H(x)x*Z(), (viii) F([x,x*])±[x,x*]Z(), (ix) F(xx*)±xx*Z(), (x) [F(x),x*]±[x,G(x*)]Z(), (xi) F(x)x*±xG(x*)Z() for all x. Finally, the restrictions imposed on the hypotheses have been justified by an example.

Keywords: Commutativity; prime ring; center; involution; commutativity; derivation; generalized derivation

MSC 2010: 16N60; 16U80; 16W25

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About the article

Received: 2017-03-03

Accepted: 2017-10-26

Published Online: 2019-10-15


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2019-2056.

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