Journal of Applied and Pure Mathematics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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MULTIPLICATIVE (GENERALIZED) (𝛼, 𝛽)-DERIVATIONS ON LEFT IDEALS IN PRIME RINGS

  • SHUJAT, FAIZA (Department of Mathematics, Faculty of Science, Taibah University)
  • Received : 2021.08.30
  • Accepted : 2021.12.07
  • Published : 2022.03.30
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Abstract

A mapping T : R → R (not necessarily additive) is called multiplicative left 𝛼-centralizer if T(xy) = T(x)𝛼(y) for all x, y ∈ R. A mapping F : R → R (not necessarily additive) is called multiplicative (generalized)(𝛼, 𝛽)-derivation if there exists a map (neither necessarily additive nor derivation) f : R → R such that F(xy) = F(x)𝛼(y) + 𝛽(x)f(y) for all x, y ∈ R, where 𝛼 and 𝛽 are automorphisms on R. The main purpose of this paper is to study some algebraic identities with multiplicative (generalized) (𝛼, 𝛽)-derivations and multiplicative left 𝛼-centralizer on the left ideal of a prime ring R.

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References

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