Some Theorems For Generalized (U,M)-Derivations In Semiprime Gamma-Rings

Authors

  • M. M. Rahman Department of Mathematics, Jagannath University, Dhaka.
  • A. C. Paul Department of Mathematics, University of Rajshahi, Rajshahi.

DOI:

https://doi.org/10.3329/jsr.v9i2.30502

Keywords:

Semiprime ?-ring, Lie ideal, Square closed Lie ideal, Admissible Lie ideal, -derivation, Generalized -derivation.

Abstract

The objective of this paper is to establish some results for generalized (U,M)-derivation in semiprime Gamma-ring, where U is a Lie ideal of a semiprime Gamma-ring. Let d be a-(U,M)-derivation and  f be a generalized (U,M)-derivation of M then we prove that

f(u?v)=f(u)?v+u?d(v) for all u,v belongs to U and a belongs to Gamma, when U is an admissible Lie ideal of M;

 f(u?m)=f(u)?m+u?d(m) for all u belongs to U, m belongs to M and a belongs to Gamma,  when U is a square closed Lie ideal of M.  

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Author Biographies

M. M. Rahman, Department of Mathematics, Jagannath University, Dhaka.

Department of Mathematics

Professor

A. C. Paul, Department of Mathematics, University of Rajshahi, Rajshahi.

Department of Mathematics

Professor

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Published

2017-04-20

How to Cite

Rahman, M. M., & Paul, A. C. (2017). Some Theorems For Generalized (U,M)-Derivations In Semiprime Gamma-Rings. Journal of Scientific Research, 9(2), 167–177. https://doi.org/10.3329/jsr.v9i2.30502

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Section

Section A: Physical and Mathematical Sciences