GENERALIZED DERIVATIONS IN RINGS ON LIE IDEALS WITH BANACH ALGEBRAS

Authors

  • Mohammad Shadab Khan
  • NADEEM UR UR REHMAN
  • MOHD ARIF RAZA

DOI:

https://doi.org/10.24297/jam.v11i1.1297

Keywords:

Banach algebras, Generalized derivations, Martindale ring of quotients, Prime and semiprime rings, Radical, Lie ideal.

Abstract

Let R be a prime ring of characteristic dierent from 2, L a non-central Lie ideal of R, and m; n xed positive integers. If R admits a generalized derivation F associated with a deviation d such that  F(u)2)m -(F(u))2n  ϵZ(R) for all u Ïµ L, then R satises S, the standard identity in four variables. Moreover, we also examine the case when R is semiprime ring. Finally, as an application we obtain some range inclusion results of continuous or spectrallybounded generalized derivations on Banach algebras.

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Published

2015-07-31

How to Cite

Khan, M. S., REHMAN, N. U. U., & RAZA, M. A. (2015). GENERALIZED DERIVATIONS IN RINGS ON LIE IDEALS WITH BANACH ALGEBRAS. JOURNAL OF ADVANCES IN MATHEMATICS, 11(1), 3948–3959. https://doi.org/10.24297/jam.v11i1.1297

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Articles