Czechoslovak Mathematical Journal

, Volume 65, Issue 1, pp 179–190 | Cite as

Generalized derivations on Lie ideals in prime rings

  • Basudeb Dhara
  • Sukhendu Kar
  • Sachhidananda Mondal
Article

Abstract

Let R be a prime ring with its Utumi ring of quotients U and extended centroid C. Suppose that F is a generalized derivation of R and L is a noncentral Lie ideal of R such that F(u)[F(u), u] n = 0 for all uL, where n ⩾ 1 is a fixed integer. Then one of the following holds:
  1. (1)

    there exists λC such that F(x) = λx for all xR

     
  2. (2)

    R satisfies s 4 and F(x) = ax + xb for all xR, with a, bU and abC

     
  3. (3)

    char(R) = 2 and R satisfies s 4.

     

As an application we also obtain some range inclusion results of continuous generalized derivations on Banach algebras.

Keywords

prime ring derivation generalized derivation extended centroid Utumi quotient ring Lie ideal Banach algebra 

MSC 2010

16W25 16W80 16N60 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2015

Authors and Affiliations

  • Basudeb Dhara
    • 1
  • Sukhendu Kar
    • 2
  • Sachhidananda Mondal
    • 2
  1. 1.Department of MathematicsBelda CollegeBelda, Paschim MedinipurIndia
  2. 2.Department of MathematicsJadavpur UniversityJadavpurIndia

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