Generalized Derivations Acting as Homomorphisms and Anti-Homomorphisms of Gamma Rings

Authors

  • K. K. Dey
  • A. C. Paul

DOI:

https://doi.org/10.3329/jsr.v4i1.7911

Keywords:

Prime Gamma-rings, generalized derivations, torsion free Gamma-rings, homomorphisms and anti-homomorphisms.

Abstract

Let M be a prime G-ring and let I be a nonzero ideal of M. Suppose that D: M ® M is a nonzero generalized derivation with associated derivation d : M ® M. Then we prove the following:

 (i) If D acts as a homomorphism on I, then either d = 0 on M or M is commutative.

(ii) If M satisfies the assumption (*) (see below), and if D acts as an anti-homomorphism on I, then either d = 0 on M or M is commutative.

Keywords: Prime G-rings; Generalized derivations; Torsion free G-rings; Homomorphisms; Anti-homomorphisms.

© 2012 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.

doi: http://dx.doi.org/10.3329/jsr.v4i1.7911

J. Sci. Res. 4 (1), 33-37 (2012)

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Author Biography

A. C. Paul

Dr. A. C. Paul

Department of Mathematics

Rajshahi University

Rajshahi, Bangladesh

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Published

2011-12-23

How to Cite

Dey, K. K., & Paul, A. C. (2011). Generalized Derivations Acting as Homomorphisms and Anti-Homomorphisms of Gamma Rings. Journal of Scientific Research, 4(1), 33. https://doi.org/10.3329/jsr.v4i1.7911

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Section

Section A: Physical and Mathematical Sciences