On derivations over trivial extensions

• boudine, brahim ^[1] ; Zerra, Mohammed
  1. [1] Faculty of sciences Dhar El Mahraz
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 43, Nº. 2, 2024, págs. 459-472
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-6040
• Enlaces
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• Resumen

  • In this paper, we investigate the structure of derivations over trivial extensions. We provide a detailed analysis of the structure of derivations on trivial extensions, the centre of trivial extensions, and the conditions for a trivial extension to be prime. Additionally, we examine the structure of derivations on trivial extensions when the underlying ring, $R$, is a prime ring, under the conditions of Herstein's Theorem, Posner's Theorem, and Bell's theorem.

• Referencias bibliográficas
  • bibitem{ADA} S. Ali, N. A. Dar, and M. Asci, textit{On derivations and commutativity of prime rings with involution}, Georgian Math. J. textbf{23}...
  • bibitem{Anderson} D. D. Anderson, and M. Winders, textit{Idealization of a module}, Journal of commutative algebra textbf{1} (2009), no. 1,...
  • bibitem{bennis2} M. A. Bahmani, D. Bennis, H. R. E. Vishki, A. E. Attar, and B. Fahid, textit{Jordan generalized derivations on trivial extension...
  • bibitem{bell} H. E. Bell, and G. Mason, textit{derivations in near-rings}, North-Holland Mathematics Studies textbf{137} (1987) 31--35.
  • bibitem{bennis1} D. Bennis, H. R. E. Vishki, B. Fahid, A. A. Khadem-Maboudi, and A. H. Mokhtari, textit{Lie generalized derivations on trivial...
  • bibitem{Bresar} M. Bresar, and J. Vukman, textit{Jordan $(theta,phi)$-derivations}, Glas. Mat. textbf{26} (1991), no. 46, 13--17.
  • bibitem{herstein} I. N. Herstein, textit{A note on derivations II}, Can. Math. Bull. textbf{22} (1979), no. 4, 509--511.
  • bibitem{Lee} P. H. Lee, and T. K. Lee, textit{On derivations of prime rings}, Chinese J. Math. textbf{9} (1981), no. 2, 107--110.
  • bibitem{MOZ1} A. Mamouni, L. Oukhtite, M. Zerra, textit{On derivations involving prime ideals and commutativity in rings}, Sao Paulo Journal...
  • bibitem{MOZ2} A. Mamouni, L. Oukhtite, M. Zerra, textit{Certain algebraic identities on prime rings with involution}, Communications in Algebra...
  • bibitem{oukhtite} M. A. Idrissi, L. Oukhtite, textit{Derivations over amalgamated algebras along an ideal}, Communications in Algebra textbf{48}...
  • bibitem{posner} E. C. Posner, textit{Derivations in prime rings}, Proc. Amer.Math. Soc. textbf{8} (1957), no. 6, 1093--1100.