On Ideals and Commutativity of Prime Rings with Generalized Derivations

Authors

  • Mohammad Khalil Abu Nawas Department of Mathematics, Faculty of Science, Northern Border University, Arar, Saudi Arabia.
  • Radwan M. Al-Omary

DOI:

https://doi.org/10.29020/nybg.ejpam.v11i1.3142

Keywords:

Left ideals, prime rings, centralizing, derivations, generalized derivations, commutativity.

Abstract

An additive mapping F: R → R is called a generalized derivation on R if there exists a derivation d: R → R such that F(xy) = xF(y) + d(x)y holds for all x,y ∈ R. It is called a generalized (α,β)−derivation on R if there exists an (α,β)−derivation d: R → R such that the equation F(xy) = F(x)α(y)+β(x)d(y) holds for all x,y ∈ R. In the present paper, we investigate commutativity of a prime ring R, which satisï¬es certain differential identities on left ideals of R. Moreover some results on commutativity of rings with involutions that satisfy certain identities are proved.

Author Biography

  • Mohammad Khalil Abu Nawas, Department of Mathematics, Faculty of Science, Northern Border University, Arar, Saudi Arabia.
    Department of Mathematics,

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Published

2018-01-30

Issue

Vol. 11 No. 1: (January 2018)

Section

Mathematical and Fuzzy Logic

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How to Cite

On Ideals and Commutativity of Prime Rings with Generalized Derivations. (2018). European Journal of Pure and Applied Mathematics, 11(1), 79-89. https://doi.org/10.29020/nybg.ejpam.v11i1.3142