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Derivations on Lie Ideals of Prime \(\varGamma \)-Rings

  • Kalyan Kumar DeyEmail author
  • Akhil Chandra Paul
  • Bijan Davvaz
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 655)

Abstract

Let M be a 2-torsion free prime \({\varGamma }\)-ring with Z(M) as the center of M. In this paper, we prove the following: (i) If U is a Lie ideal of M and if \(d\not =0\) is a derivation of M such that \(d^2(U) = 0\), then \(U\subseteq Z(M)\); (ii) if \(U\not \subset Z(M)\) is a Lie ideal of M and \(d\not =0\) is a derivation of M, then \(Z(d(U))\subseteq Z(M)\); (iii) If \(U\not \subset Z(M)\) is a Lie ideal of M and if d is a derivation of M such that \(d^3\not = 0\), then \(d(U)^*\), the subring generated by d(U) contains a non-zero ideal of M. Finally, we prove that if \(U \not \subset Z(M)\) is a Lie ideal of M and \(d_1\) and \(d_2\) are derivations of M such that \(d_1d_2(U) = 0\), then \(d_1 = 0\) or \(d_2 = 0\).

Keywords

\(\varGamma \)-ring Prime \(\varGamma \)-ring Derivation \({\varGamma }\)-Lie ideal 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  • Kalyan Kumar Dey
    • 1
    Email author
  • Akhil Chandra Paul
    • 1
  • Bijan Davvaz
    • 2
  1. 1.Department of MathematicsRajshahi UniversityRajshahiBangladesh
  2. 2.Department of MathematicsYazd UniversityYazdIran

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