Some Characterizations on Actions of Generalized Derivations AsHomomorphisms And Anti-Homomorphisms In SemiprimeGamma Rings

Authors

  • Sujoy Chakraborty Department of Mathematics, Shahjalal University of Science and Technology, Sylhet, Bangladesh
  • Akhil Chandra Paul Department of Mathematics, University of Rajshahi, Rajshahi-6205, Bangladesh

DOI:

https://doi.org/10.3329/ganit.v42i1.60998

Keywords:

Gamma ring; generalized derivation; homomorphism.

Abstract

Let I be a non-zero left ideal of a r-ring M satisfying the condition alpha alpha b beta c= a beta b alpha c for all a,b,c, e M and alpha, beta e r. We show that M contains a non-trivial central ideal if M is semiprime which admits an appropriate non-zero derivations on I, and also that M is commutative if M is prime admitting a non-zero centralizing derivation on I. We next give some characterizations when non-zero generalized derivations act as homomorphisms and as anti-homomorphisms on some non-zero left or two-sided ideals of semiprime gamma rings, somewhere of prime gamma rings also, satisfying the above condition.
GANIT J. Bangladesh Math. Soc. 42.1 (2022) 025- 034

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Published

2022-08-22

How to Cite

Chakraborty, S. ., & Paul, A. C. . (2022). Some Characterizations on Actions of Generalized Derivations AsHomomorphisms And Anti-Homomorphisms In SemiprimeGamma Rings. GANIT: Journal of Bangladesh Mathematical Society, 42(1), 025–034. https://doi.org/10.3329/ganit.v42i1.60998

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